SOLUTION: Find the inverse of the function f(x)=8^(4x+9)

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Question 211681: Find the inverse of the function f(x)=8^(4x+9)
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=8%5E%284x%2B9%29
f%28x%29=8%5E%284x%29+%2A+8%5E9
f%28x%29=%288%5E4%29%5Ex+%2A+8%5E9
f%28x%29=%288%5E4%29%5Ex+%2A+8%5E9
8%5E-9+%2A+f%28x%29=%288%5E4%29%5Ex
log_8%5E4 8%5E-9+%2A+f%28x%29=x
log_8%5E48%5E-9 + log_8%5E4 f(x)=x
(-9/4) + log_8%5E4f(x)=x
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So the inverse function is,
f%5E-1%28x%29=%28-9%2F4%29+%2B+log_4096+%28x%29