Question

What is the value of X if 9^x^-^1-2=25?

Answer 1

Answer:

$\frac{5}{2}$

Step-by-step explanation:

First, add two to both sides to get $9^{x-1}=27$

There are two ways to solve this from here

1. Think about what power you would have to raise 9 to to get to 27. $9^{\frac{1}{2}}$ = 3 and $3^3=27$. So, multiplying the powers (because it is a power to a power) you get $9^{\frac{3}{2}}=27$. This means that $x - 1 = \frac{3}{2}$ or x = $\frac{5}{2}$.
2. Take the log of both sides.

This gives us $\log_9(27)=x-1\\\log_9(27)+1=x\\\log_9(3^3)+1=x\\3\log_9(3)+1=x\\3(\frac{1}{2})+1=x\\\frac{3}{2}+1 = x\\\\\frac{5}{2} = x$