Solvie Exponential functions: 1/81=27^x-2

[scoobyrunswild]

I have 1/81=27^x-2

Can someone show me how to begin solving this problem? I am totally stuck!

Thank you

 

[soroban]

Re: Solvie Exponential functions

Hello, scoobyrunswild!

Solve for \(\displaystyle x:\;\;\frac{1}{81}\;=\;27^{x-2}\)

We have: \(\displaystyle \L\:27^{x-2} \;=\;\frac{1}{81}\;\;\Rightarrow\;\;(3^3)^{x-2} \;=\;\frac{1}{3^4}\;\;\Rightarrow\;\;3^{3x-6}\;=\;3^{-4}\)

The bases are equal, so the exponents are equal: \(\displaystyle \L\:3x\,-\,6\;=\;-4\)

Now solve for \(\displaystyle \L x\) . . .

 

[scoobyrunswild]

Thank you, soroban!!! :lol: