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

Question

anonymous · Answer

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

anonymous · Answer

@zepdrix help please?

kainui · Answer

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:

$$ \log_2(x) = y$$

anonymous · Answer

Okay well that kinda makes sense

anonymous · Answer

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 · Answer

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.