how do you convert the function f(x)=15^x into a logarithmic one?

Question

kmeis002 · Answer

Do you mean, how do you solve for x?

xapproachesinfinity · Answer

think about this $$a^b=n \Longrightarrow \log_b(n)=a$$

anonymous · Answer

so then you would get log(base)x(f(x))=15?

xapproachesinfinity · Answer

this one for natural log $$\ln x=y \Longrightarrow e^y=x$$

xapproachesinfinity · Answer

no use the equation $$y=15^x$$

xapproachesinfinity · Answer

eh it really doen't matter what you choose as a base and exponent

xapproachesinfinity · Answer

oh i made a mistake with the base lol

solomonzelman · Answer

yes, that is what I was about to post...

solomonzelman · Answer

I thought
$\large\color{black}{ \displaystyle a^b=n   }$
$\large\color{black}{ \displaystyle \log_aa^b=log_an   }$
$\large\color{black}{ \displaystyle b=log_an   }$

solomonzelman · Answer

forgot the backwards slash next to logs, sorry for my bad latex.

xapproachesinfinity · Answer

again i wrote the same thing i must of drunk

solomonzelman · Answer

$\large\color{black}{ \displaystyle a^b=n   }$

$\large\color{black}{ \displaystyle \log_a(a^b)=\log_a(n)   }$

$\large\color{black}{ \displaystyle b\log_a(a)=\log_a(n)   }$

$\large\color{black}{ \displaystyle b=\log_a(n)   }$

solomonzelman · Answer

It happens to me all the time, and I would bet more than to you.

xapproachesinfinity · Answer

yep it should be $$a^b=n \Longrightarrow \log_a(n)=b$$

xapproachesinfinity · Answer

does not happen to me usually lol
just my brain is burned today hahah

xapproachesinfinity · Answer

so if we have $$y=15^x \Longrightarrow \log_{15}(y)=x$$
just switch x and y and you get $$y=\log_{15}x$$

xapproachesinfinity · Answer

that is the function you are looking for