Question

Select the correct answer.

Answer 1

9514 1404 393

Answer:

  B.  1/2

Step-by-step 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.

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

Using logarithms, the solution looks like ...

  $x\cdot\log{9}=\log{3}\\\\x=\dfrac{\log{3}}{\log{9}}=\dfrac{1}{2}$