Chapter 4, Problem 70RE

To determine

To Find: The solution of the equation.

Answer to Problem 70RE

  $x\approx 2.602451$

Explanation of Solution

Given:Use a calculator to find the solution of the equation, rounded to the six decimals.

  $2^{3x-5}=7$

FORMULA USED:

  $\begin{array}{l}\text{Properties of logarithms:}\\ \log a^x=x\log a\end{array}$

Given: $2^{3x-5}=7$

Taking the logarithm both sides

  $\log 2^{3x-5}=\log 7$

Using the properties of logarithm

  $\begin{array}{l}\log 2^{3x-5}=\log 7\\ (3x-5)\log 2=log7\\ 3x\log 2-5\log 2=\log 7\\ 3x\log 2=\log 7+5\log 2\\ x=\frac{\log 7+5\log 2}{3\log 2}\approx 2.602451\\ i.e\\ x\approx 2.602451\end{array}$

Hence, the solution of the equation is $x\approx 2.602451$