Question

prove the rule:

Answer 1

\[a^{x}=\exp(xlna)\]

Answer 2

and \[\log _{a}=\frac{ lnx }{ lna }\]

Answer 3

\[e^{xlna}=(e^{lna})^x=(e^{\log_ea})^x=a^x\]

Answer 4

For the second, do you mean\[\log_a x=\frac{lnx}{lna}\]?

Answer 5

\[\large \log_a x= \log_{a^{\log_a e}}x^{\log_a e}=\ln x^{\log_a e}\]

Answer 6

\[\large \ln x^{\log_a e} ln a= lnx\]
\[\large ( x^{\log_a e} + a)=x\]

Answer 7

\[\large x^{\log_a e}=x-a\]
\[\large x^{\log_a e}=x^{log_x{(x-a)}}\]
\[\large {\log_a e}={log_x{x-a}}\]

Answer 8

@henpen , yes sorry i forgot the x

Answer 9

I'm not quite sure where to go after that

Answer 10

am not sure i follow ur steps.. how did you get all the those terms in the first part?