I need help with inverses of log functions. I'll put the question below.

Question

anonymous · Answer

Find the inverse of the function. $$\log_{4} x$$

I thought it was y=4^x but apparently not?

dr0zier99 · Answer

no

solomonzelman · Answer

For example if,
$\color{#000000 }{ \displaystyle r=\log_a(t)  }$

Then,
$\color{#000000 }{ \displaystyle a^r=t  }$
would be the inverse.

solomonzelman · Answer

Another example;
$\color{#000000 }{ \displaystyle \log_{14}{z} =Q\quad \Longrightarrow\quad  14^{Q}=z }$

anonymous · Answer

Do you think there was a mistake in my practice quiz? y=x^4 is the correct answer, but the base in the log function is 4.

anonymous · Answer

When you arrive at x=4^y, is there something you have to do to make it y=x^4 instead? Is that it?

solomonzelman · Answer

$x=4^y$ is right!
But your other options are all wrong (including the one you entered)

solomonzelman · Answer

$\color{#000000 }{ \displaystyle \log_4x=y\quad \Longrightarrow \quad  4^y=x }$

anonymous · Answer

Thank you, I understand now! I think they might be trying to put the answer in the proper exponential form with the x and y having different meanings than before. I'll make sure to ask my teacher.

solomonzelman · Answer

Yes, ask the instructor:)
Good Luck!