Question

Select the correct answer.

What is the solution to this equation?
g^x-1=2

A. -1/2
B. 1/2
C. 2
D. 1

Answer 1

9514 1404 393

Answer:

B. 1/2

Explanation:

Maybe you want the solution to ...

`9^x-1=2`

You can use logarithms, or your knowledge of powers of 3 to solve this.

`9^x=3\qquad\text{add 1}\\\\3^(2x)=3^1\qquad\text{express as powers of 3}\\\\2x=1\qquad\text{equate exponents of the same base}\\\\\boxed{x=(1)/(2)}\qquad\text{divide by 2}`

Using logarithms, the solution looks like ...

`x\cdot\log{9}=\log{3}\\\\x=\frac{\log{3}}{\log{9}}=(1)/(2)`