BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 6.6, Problem 72E

To determine

To calculate: .The equation for the value of $x$ .

Expert Solution & Answer

Answer to Problem 72E

The required value of $x$ is $1$ .

Explanation of Solution

Given Information:

The given equation is $52x+20⋅5x−125=0$ .

Formula Used:

Power rule of logarithmic functions.

$logaxp=plogax$

Where $a$ is the base, $x$ is the variable and $p$ is the power of variable.

Property of logarithm.

$logaa=1$

Quadratic formula.

If $ax2+bx+c=0$ then $x=−b±b2−4ac2a$

Where $a,b,c$ are constant and $a≠0$

Calculation:

Consider the equation is $52x+20⋅5x−125=0$ .

Substitute $y$ for $5x$ in the above equation.

$y2+20y−125=0$

Use quadratic formula of the above equation.

$y=−b±b2−4ac2a$

Substitute $1$ for $a$ , $20$ for $b$ and $−125$ for $c$ in the above formula.

$y=−20±(20)2−4(1)(−125)2(1)$

Simplify the above equation.

$y=−20±(20)2−4(1)(−125)2(1)=−20±400+5002=−20±9002=−20±302$

Simplify the equation.

$y=−20±302=−20+302,−20−302=102.−502=5,−25$

Now, $y=5$

Substitute $5x$ for $y$ in the above result.

$5x=5$

Take logarithm each side with base $5$ .

$log55x=log55$

Use power rule of logarithm $logaxp=plogax$ in the above equation.

$xlog55=log55$

Use property of logarithm $logaa=1$ in the above equation.

$x(1)=1x=1$

And

$y=−25$

Substitute $5x$ for $y$ in the above result.

$5x=−25$

Take logarithm each side with base $5$ .

$log55x=log5(−25)$

It is known that $loga(−x)$ is does not exist.

Hence, the required value of $x$ is $1$ .

Chapter 6.6, Problem 71E

Chapter 6.6, Problem 73E

Chapter 6 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - Prob. 60E Ch. 6.2 - Prob. 1E Ch. 6.2 - Prob. 2E Ch. 6.2 - Prob. 3E Ch. 6.2 - Prob. 4E Ch. 6.2 - Prob. 5E Ch. 6.2 - Prob. 6E Ch. 6.2 - Prob. 7E Ch. 6.2 - Prob. 8E Ch. 6.2 - Prob. 9E Ch. 6.2 - Prob. 10E Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Prob. 13E Ch. 6.2 - Prob. 14E Ch. 6.2 - Prob. 15E Ch. 6.2 - Prob. 16E Ch. 6.2 - Prob. 17E Ch. 6.2 - Prob. 18E Ch. 6.2 - Prob. 19E Ch. 6.2 - Prob. 20E Ch. 6.2 - Prob. 21E Ch. 6.2 - Prob. 22E Ch. 6.2 - Prob. 23E Ch. 6.2 - Prob. 24E Ch. 6.2 - Prob. 25E Ch. 6.2 - Prob. 26E Ch. 6.2 - Prob. 27E Ch. 6.2 - Prob. 28E Ch. 6.2 - Prob. 29E Ch. 6.2 - Prob. 30E Ch. 6.2 - Prob. 31E Ch. 6.2 - Prob. 32E Ch. 6.2 - Prob. 33E Ch. 6.2 - Prob. 34E Ch. 6.2 - Prob. 35E Ch. 6.2 - Prob. 36E Ch. 6.2 - Prob. 37E Ch. 6.2 - Prob. 38E Ch. 6.2 - Prob. 39E Ch. 6.2 - Prob. 40E Ch. 6.2 - Prob. 41E Ch. 6.2 - Prob. 42E Ch. 6.2 - Prob. 43E Ch. 6.2 - Prob. 44E Ch. 6.2 - Prob. 45E Ch. 6.2 - Prob. 46E Ch. 6.2 - Prob. 47E Ch. 6.2 - Prob. 48E Ch. 6.2 - Prob. 49E Ch. 6.2 - Prob. 50E Ch. 6.2 - Prob. 51E Ch. 6.3 - Prob. 1E Ch. 6.3 - Prob. 2E Ch. 6.3 - Prob. 3E Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 21E Ch. 6.3 - Prob. 22E Ch. 6.3 - Prob. 23E Ch. 6.3 - Prob. 24E Ch. 6.3 - Prob. 25E Ch. 6.3 - Prob. 26E Ch. 6.3 - Prob. 27E Ch. 6.3 - Prob. 28E Ch. 6.3 - Prob. 29E Ch. 6.3 - Prob. 30E Ch. 6.3 - Prob. 31E Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Prob. 39E Ch. 6.3 - Prob. 40E Ch. 6.3 - Prob. 41E Ch. 6.3 - Prob. 42E Ch. 6.3 - Prob. 43E Ch. 6.3 - Prob. 44E Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.3 - Prob. 49E Ch. 6.3 - Prob. 50E Ch. 6.3 - Prob. 51E Ch. 6.3 - Prob. 52E Ch. 6.3 - Prob. 53E Ch. 6.3 - Prob. 54E Ch. 6.3 - Prob. 55E Ch. 6.3 - Prob. 56E Ch. 6.3 - Prob. 57E Ch. 6.3 - Prob. 58E Ch. 6.3 - Prob. 59E Ch. 6.3 - Prob. 60E Ch. 6.3 - Prob. 61E Ch. 6.3 - Prob. 62E Ch. 6.3 - Prob. 63E Ch. 6.3 - Prob. 64E Ch. 6.3 - Prob. 65E Ch. 6.3 - Prob. 66E Ch. 6.3 - Prob. 67E Ch. 6.3 - Prob. 68E Ch. 6.3 - Prob. 69E Ch. 6.3 - Prob. 70E Ch. 6.3 - Prob. 71E Ch. 6.3 - Prob. 72E Ch. 6.3 - Prob. 73E Ch. 6.3 - Prob. 74E Ch. 6.3 - Prob. 75E Ch. 6.3 - Prob. 76E Ch. 6.3 - Prob. 77E Ch. 6.3 - Prob. 78E Ch. 6.4 - Prob. 1E Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - Prob. 5E Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 9E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - Prob. 14E Ch. 6.4 - Prob. 15E Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.4 - Prob. 18E Ch. 6.4 - Prob. 19E Ch. 6.4 - Prob. 20E Ch. 6.4 - Prob. 21E Ch. 6.4 - Prob. 22E Ch. 6.4 - Prob. 23E Ch. 6.4 - Prob. 24E Ch. 6.4 - Prob. 25E Ch. 6.4 - Prob. 26E Ch. 6.4 - Prob. 27E Ch. 6.4 - Prob. 28E Ch. 6.4 - Prob. 29E Ch. 6.4 - Prob. 30E Ch. 6.4 - Prob. 31E Ch. 6.4 - Prob. 32E Ch. 6.4 - Prob. 33E Ch. 6.4 - Prob. 34E Ch. 6.4 - Prob. 35E Ch. 6.4 - Prob. 36E Ch. 6.4 - Prob. 37E Ch. 6.4 - Prob. 38E Ch. 6.4 - Prob. 39E Ch. 6.4 - Prob. 40E Ch. 6.4 - Prob. 41E Ch. 6.4 - Prob. 42E Ch. 6.4 - Prob. 43E Ch. 6.4 - Prob. 44E Ch. 6.4 - Prob. 45E Ch. 6.4 - Prob. 46E Ch. 6.4 - Prob. 47E Ch. 6.4 - Prob. 48E Ch. 6.4 - Prob. 49E Ch. 6.4 - Prob. 50E Ch. 6.4 - Prob. 51E Ch. 6.4 - Prob. 52E Ch. 6.4 - Prob. 53E Ch. 6.4 - Prob. 54E Ch. 6.4 - Prob. 55E Ch. 6.4 - Prob. 56E Ch. 6.4 - Prob. 57E Ch. 6.4 - Prob. 58E Ch. 6.4 - Prob. 59E Ch. 6.4 - Prob. 60E Ch. 6.4 - Prob. 1Q Ch. 6.4 - Prob. 2Q Ch. 6.4 - Prob. 3Q Ch. 6.4 - Prob. 4Q Ch. 6.4 - Prob. 5Q Ch. 6.4 - Prob. 6Q Ch. 6.4 - Prob. 7Q Ch. 6.4 - Prob. 8Q Ch. 6.4 - Prob. 9Q Ch. 6.4 - Prob. 10Q Ch. 6.4 - Prob. 11Q Ch. 6.4 - Prob. 12Q Ch. 6.4 - Prob. 13Q Ch. 6.4 - Prob. 14Q Ch. 6.4 - Prob. 15Q Ch. 6.4 - Prob. 16Q Ch. 6.4 - Prob. 17Q Ch. 6.4 - Prob. 18Q Ch. 6.4 - Prob. 19Q Ch. 6.4 - Prob. 20Q Ch. 6.4 - Prob. 21Q Ch. 6.4 - Prob. 22Q Ch. 6.4 - Prob. 23Q Ch. 6.4 - Prob. 24Q Ch. 6.4 - Prob. 25Q Ch. 6.4 - Prob. 26Q Ch. 6.5 - Prob. 1E Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6.5 - Prob. 16E Ch. 6.5 - Prob. 17E Ch. 6.5 - Prob. 18E Ch. 6.5 - Prob. 19E Ch. 6.5 - Prob. 20E Ch. 6.5 - Prob. 21E Ch. 6.5 - Prob. 22E Ch. 6.5 - Prob. 23E Ch. 6.5 - Prob. 24E Ch. 6.5 - Prob. 25E Ch. 6.5 - Prob. 26E Ch. 6.5 - Prob. 27E Ch. 6.5 - Prob. 28E Ch. 6.5 - Prob. 29E Ch. 6.5 - Prob. 30E Ch. 6.5 - Prob. 31E Ch. 6.5 - Prob. 32E Ch. 6.5 - Prob. 33E Ch. 6.5 - Prob. 34E Ch. 6.5 - Prob. 35E Ch. 6.5 - Prob. 36E Ch. 6.5 - Prob. 37E Ch. 6.5 - Prob. 38E Ch. 6.5 - Prob. 39E Ch. 6.5 - Prob. 40E Ch. 6.5 - Prob. 41E Ch. 6.5 - Prob. 42E Ch. 6.5 - Prob. 43E Ch. 6.5 - Prob. 44E Ch. 6.5 - Prob. 45E Ch. 6.5 - Prob. 46E Ch. 6.5 - Prob. 47E Ch. 6.5 - Prob. 48E Ch. 6.5 - Prob. 49E Ch. 6.5 - Prob. 50E Ch. 6.5 - Prob. 51E Ch. 6.5 - Prob. 52E Ch. 6.5 - Prob. 53E Ch. 6.5 - Prob. 54E Ch. 6.5 - Prob. 55E Ch. 6.5 - Prob. 56E Ch. 6.6 - Prob. 1E Ch. 6.6 - Prob. 2E Ch. 6.6 - Prob. 3E Ch. 6.6 - Prob. 4E Ch. 6.6 - Prob. 5E Ch. 6.6 - Prob. 6E Ch. 6.6 - Prob. 7E Ch. 6.6 - Prob. 8E Ch. 6.6 - Prob. 9E Ch. 6.6 - Prob. 10E Ch. 6.6 - Prob. 11E Ch. 6.6 - Prob. 12E Ch. 6.6 - Prob. 13E Ch. 6.6 - Prob. 14E Ch. 6.6 - Prob. 15E Ch. 6.6 - Prob. 16E Ch. 6.6 - Prob. 17E Ch. 6.6 - Prob. 18E Ch. 6.6 - Prob. 19E Ch. 6.6 - Prob. 20E Ch. 6.6 - Prob. 21E Ch. 6.6 - Prob. 22E Ch. 6.6 - Prob. 23E Ch. 6.6 - Prob. 24E Ch. 6.6 - Prob. 25E Ch. 6.6 - Prob. 26E Ch. 6.6 - Prob. 27E Ch. 6.6 - Prob. 28E Ch. 6.6 - Prob. 29E Ch. 6.6 - Prob. 30E Ch. 6.6 - Prob. 31E Ch. 6.6 - Prob. 32E Ch. 6.6 - Prob. 33E Ch. 6.6 - Prob. 34E Ch. 6.6 - Prob. 35E Ch. 6.6 - Prob. 36E Ch. 6.6 - Prob. 37E Ch. 6.6 - Prob. 38E Ch. 6.6 - Prob. 39E Ch. 6.6 - Prob. 40E Ch. 6.6 - Prob. 41E Ch. 6.6 - Prob. 42E Ch. 6.6 - Prob. 43E Ch. 6.6 - Prob. 44E Ch. 6.6 - Prob. 45E Ch. 6.6 - Prob. 46E Ch. 6.6 - Prob. 47E Ch. 6.6 - Prob. 48E Ch. 6.6 - Prob. 49E Ch. 6.6 - Prob. 50E Ch. 6.6 - Prob. 51E Ch. 6.6 - Prob. 52E Ch. 6.6 - Prob. 53E Ch. 6.6 - Prob. 54E Ch. 6.6 - Prob. 55E Ch. 6.6 - Prob. 56E Ch. 6.6 - Prob. 57E Ch. 6.6 - Prob. 58E Ch. 6.6 - Prob. 59E Ch. 6.6 - Prob. 60E Ch. 6.6 - Prob. 61E Ch. 6.6 - Prob. 62E Ch. 6.6 - Prob. 63E Ch. 6.6 - Prob. 64E Ch. 6.6 - Prob. 65E Ch. 6.6 - Prob. 66E Ch. 6.6 - Prob. 67E Ch. 6.6 - Prob. 68E Ch. 6.6 - Prob. 69E Ch. 6.6 - Prob. 70E Ch. 6.6 - Prob. 71E Ch. 6.6 - Prob. 72E Ch. 6.6 - Prob. 73E Ch. 6.6 - Prob. 74E Ch. 6.6 - Prob. 75E Ch. 6.6 - Prob. 76E Ch. 6.6 - Prob. 77E Ch. 6.6 - Prob. 78E Ch. 6.6 - Prob. 79E Ch. 6.6 - Prob. 80E Ch. 6.6 - Prob. 81E Ch. 6.7 - Prob. 1E Ch. 6.7 - Prob. 2E Ch. 6.7 - Prob. 3E Ch. 6.7 - Prob. 4E Ch. 6.7 - Prob. 5E Ch. 6.7 - Prob. 6E Ch. 6.7 - Prob. 7E Ch. 6.7 - Prob. 8E Ch. 6.7 - Prob. 9E Ch. 6.7 - Prob. 10E Ch. 6.7 - Prob. 11E Ch. 6.7 - Prob. 12E Ch. 6.7 - Prob. 13E Ch. 6.7 - Prob. 14E Ch. 6.7 - Prob. 15E Ch. 6.7 - Prob. 16E Ch. 6.7 - Prob. 17E Ch. 6.7 - Prob. 18E Ch. 6.7 - Prob. 19E Ch. 6.7 - Prob. 20E Ch. 6.7 - Prob. 21E Ch. 6.7 - Prob. 22E Ch. 6.7 - Prob. 23E Ch. 6.7 - Prob. 24E Ch. 6.7 - Prob. 25E Ch. 6.7 - Prob. 26E Ch. 6.7 - Prob. 27E Ch. 6.7 - Prob. 28E Ch. 6.7 - Prob. 29E Ch. 6.7 - Prob. 30E Ch. 6.7 - Prob. 31E Ch. 6.7 - Prob. 32E Ch. 6.7 - Prob. 33E Ch. 6.7 - Prob. 34E Ch. 6.7 - Prob. 35E Ch. 6.7 - Prob. 36E Ch. 6.7 - Prob. 37E Ch. 6.7 - Prob. 38E Ch. 6.7 - Prob. 39E Ch. 6.7 - Prob. 40E Ch. 6.7 - Prob. 41E Ch. 6.7 - Prob. 42E Ch. 6.7 - Prob. 43E Ch. 6.7 - Prob. 44E Ch. 6.7 - Prob. 45E Ch. 6.7 - Prob. 46E Ch. 6.7 - Prob. 47E Ch. 6 - Prob. 1CR Ch. 6 - Prob. 2CR Ch. 6 - Prob. 3CR Ch. 6 - Prob. 4CR Ch. 6 - Prob. 5CR Ch. 6 - Prob. 6CR Ch. 6 - Prob. 7CR Ch. 6 - Prob. 8CR Ch. 6 - Prob. 9CR Ch. 6 - Prob. 10CR Ch. 6 - Prob. 11CR Ch. 6 - Prob. 12CR Ch. 6 - Prob. 13CR Ch. 6 - Prob. 14CR Ch. 6 - Prob. 15CR Ch. 6 - Prob. 16CR Ch. 6 - Prob. 17CR Ch. 6 - Prob. 18CR Ch. 6 - Prob. 19CR Ch. 6 - Prob. 20CR Ch. 6 - Prob. 21CR Ch. 6 - Prob. 22CR Ch. 6 - Prob. 23CR Ch. 6 - Prob. 24CR Ch. 6 - Prob. 25CR Ch. 6 - Prob. 26CR Ch. 6 - Prob. 27CR Ch. 6 - Prob. 28CR Ch. 6 - Prob. 29CR Ch. 6 - Prob. 30CR Ch. 6 - Prob. 31CR Ch. 6 - Prob. 32CR Ch. 6 - Prob. 33CR Ch. 6 - Prob. 34CR Ch. 6 - Prob. 35CR Ch. 6 - Prob. 36CR Ch. 6 - Prob. 37CR Ch. 6 - Prob. 38CR Ch. 6 - Prob. 39CR Ch. 6 - Prob. 1CT Ch. 6 - Prob. 2CT Ch. 6 - Prob. 3CT Ch. 6 - Prob. 4CT Ch. 6 - Prob. 5CT Ch. 6 - Prob. 6CT Ch. 6 - Prob. 7CT Ch. 6 - Prob. 8CT Ch. 6 - Prob. 9CT Ch. 6 - Prob. 10CT Ch. 6 - Prob. 11CT Ch. 6 - Prob. 12CT Ch. 6 - Prob. 13CT Ch. 6 - Prob. 14CT Ch. 6 - Prob. 15CT Ch. 6 - Prob. 1CA Ch. 6 - Prob. 2CA Ch. 6 - Prob. 3CA Ch. 6 - Prob. 4CA Ch. 6 - Prob. 5CA Ch. 6 - Prob. 6CA Ch. 6 - Prob. 7CA Ch. 6 - Prob. 8CA Ch. 6 - Prob. 9CA

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

.The equation for the value of x .