Answered: In Problem write the equation in…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

In Problem write the equation in logarithmic form and solve for x.

10^2x+1 = 0.25 (to 3 decimal places)

Expert Solution

Step 1

Given equation is $10^{2 x + 1} = 0.25$ .

To write the equation in logarithm form and then solve for $x$ .

Solution:

Equation is $10^{2 x + 1} = 0.25$ .

Taking logarithm on both sides, we get

$\log {(10)}^{2 x + 1} = \log (0.25)$

Now, solving the equation.

$\begin{array}{rcl} \log {(10)}^{2 x + 1} & = & \log (0.25) \\ (2 x + 1) \log (10) & = & \log (\frac{25}{100}) [Using \log m^{n} = n \log m] \\ (2 x + 1) \cdot 1 & = & \log (\frac{1}{4}) [Using \log 10 = 1] \\ 2 x + 1 & = & \log 1 - \log 4 [Using \log (\frac{m}{n}) = \log m - \log n] \\ 2 x + 1 & = & 0 - 0.602 \\ 2 x & = & - 0.602 - 1 \\ 2 x & = & - 1.602 \\ x & = & - \frac{1.602}{2} \\ x & = & - 0.801 \end{array}$

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