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- anonymous

is anyone good with Inverse of exponential functions? If so can someone help me with a few questions? I will fan and medal.

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- anonymous

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- anonymous

Given f(x)=3^x, find f^–1(x) and f^–1(27).

- anonymous

@zepdrix help please?

- Kainui

The inverse of an exponential function is a logarithm, they're sorta weird if you're new to them, so here's an example:
\[ \log_2(8)\]
The little 2 on the log is the base, and this is basically saying, "what power of 2 is this?" So since \(8=2^3\) then we can write:
\[ \log_2(8)=3\]
so the trick is if we have something like \(y=2^x\) the inverse will be to take the logarithm base 2 of both sides since:
\[ \log_2(y) = \log_2(2^x)\]
Notice that right side is saying what's the power on \(2^x\) ? Well that's just x! So we rewrite it:
\[ \log_2(y) = x\]
Since this is the inverse function we switch y and x (or in your case f(x) and x. to get:
\[ \log_2(x) = y\]

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- anonymous

Okay well that kinda makes sense

- anonymous

but can you like sorta walk me through this one? Given f(x)=3^x, find f^–1(x) and f^–1(27). @Kainui

- Kainui

Well I walked you through some stuff right there, see if you can take what I'm saying and apply it to solve your problem first and I'll help you.

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