Question

Explain how to solve 2^x + 1 = 9 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Answer:

$x=2.170$

Step-by-step explanation:

The given equation is $2^{x+1}=9$.

We take logarithm of both sides to base 2 to get:

$\log_2(2^{x+1})=\log_29$

Apply the power rule of logarithms to get:

$x+1=\log_29$

We now apply the change of base formula:

$x+1=\frac{\log_{10}9}{\log_{10}2}$

$x+1=\frac{0.9542}{0.3010}$

$x+1=3.1701$

$x=3.1701-1$

$x=2.1701$

To the nearest thousandth, $x=2.170$