Question

I really don't understand logarithms... I have two questions and I would really appreciate if someone could explain them to me and help me!!

1. Rewrite log 2(64)=6 as an exponential.
(Read log base 2 of 64)
2. Rewrite x=a^y as an logarithm.

Thank you in advance!! :)

Answer 1

There is a rule:

\(\Large\color{black}{ \displaystyle \log_{\color{red}{\rm A}}\left(\color{green}{\rm B}\right)=\color{blue}{\rm C}{~~~~~~} _{\Huge ~~\Longrightarrow}^{\rm converts~to }{~~~~~~} \color{red}{\rm A}^\color{blue}{\rm C}=\color{green}{\rm B}}\)

Answer 2

For example,

\(\large\color{black}{ \displaystyle \log_3x=4 }\)
would convert to
\(\large\color{black}{ \displaystyle 3^4=x }\)
and then
\(\large\color{black}{ \displaystyle x=81 }\)

Answer 3

That was very helpful, thank you- but I don't see how that helps when they're not in logarithmic form..

Answer 4

Well, when one isn't? Idk- this is very confusing for me

Answer 5

So if log 2(64)=6, does that change it to 2^6=64? Do I have to solve for it?

Answer 6

yes 2\(^6\)=64 is the correct conversion

Answer 7

and you don't need to solve for anything here:)
2\(^6\) = (2\(^3\))\(^2\) = 8\(^2\) = 64,
so you know it is true...