SOLUTION: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!! Laws of Loga

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Question 197090This question is from textbook Algebra and Trigonometry Structure and Method book 2
: I have been working on this math problem and I can't figure it out. I was wondering if someone could help me? Please and Thank You!! I would deeply appreciate it!!
Laws of Logarithms
If f(x)=3^x and g(x)=log base 9 of x, find:
f^-1(g(9)) This question is from textbook Algebra and Trigonometry Structure and Method book 2

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
If f(x)=3^x and
g(x)=log base 9 of x, find:
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You need f^(-1)(x)
Starting with f(x) = 3^x
Interchange x and y to get:
x = 3^y
Solve for y:
y = log(base3)x
So f^(-1)(x) = log(base3)x
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Now try your problem:
f^-1(g(9)) = f^(-1)[log(base9)9]
= f^(-1)[1]
= log(base3)1
= 0
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That's pretty complicated. Hope that helps.
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Cheers,
Stan H.