SOLUTION: The instructions say for each function, find f^-1. Help please, step by step. Thank you... f(x)= 6^x-1 Also, solve each equation. Find the Exact solutions. 1/2^x = 5 t

Question 149457This question is from textbook
: The instructions say for each function, find f^-1. Help please, step by step. Thank you...
f(x)= 6^x-1
Also, solve each equation. Find the Exact solutions.
1/2^x = 5 the exponent is above the 2 only. This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given function.

Switch x and f(x).

Take the log of both sides.

Rewrite the right side using the identity

Distribute

Add to both sides.

Combine the logs using the identity

Divide both sides by to isolate f(x)

Use the change of base formula to rewrite the left side.

So the inverse function is

Start with the given equation.

Multiply both sides by .

Divide both sides by .

Take the log of both sides.

Rewrite the right side using the identity

Divide both sides by to isolate x

Use the change of base formula to rewrite the left side.

So the answer is which approximates to
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