Question

How do I simplify this? 4^(log4(x+3))

Answer 1

\(\bf \large {{\color{red}{ a}}^y={\color{blue}{ b}}\implies log_{\color{red}{ a}}{\color{blue}{ b}}=y
\\ \quad \\ \quad \\
{\color{red}{ 4}}^{log_{\color{red}{ 4}}(x+3)}= \square \implies log_{\color{red}{ 4}}{\color{blue}{ \square }}=log_{\color{red}{ 4}}(x+3) }\)

what do you think?

Answer 2

\[a^{\log_a(f(x))}=f(x) , f(x)>0, a \in (0,1)\cup (1,\infty)\]

Answer 3

or you can always keep in mind that \(\Large \bf \textit{log cancellation rule of }\quad {\color{red}{ a}}^{log_{\color{red}{ a}}x}=x\)

Answer 4

since y=a^x and y=log_a(x) are inverses

Answer 5

I still dont understand, can you provide an example please?

Answer 6

example:
\[a^{\log_a( \text{ candy} } ) =\text{ candy }\]

Answer 7

ohh, I see. Thank you.

Answer 8

so what do you think your answer is?

Answer 9

X+3?

Answer 10

yep

Answer 11

Does this also work for log10^(10^3x+1)

Answer 12

and the answer would be 3x+1?