Question

how do i use logarithms to solve the equation 2^=14

Answer 1

\(\bf 2^x=14\quad ?\)

Answer 2

what do you mean by "solve"?

Answer 3

i need to use logarithms to solve this equation

Answer 4

\(\bf 2^x=14\quad ?\) <---- is that what you meant?

Answer 5

yes looking to solve for what x is in logorithm form

Answer 6

Hint...

\[\large \ln a^x => x \times \ln a\]

Answer 7

you could also use the log cancellation rule of \(\bf log_{\color{red}{ a}}{\color{red}{ a}}^x=x\)

Answer 8

thank you

Answer 9

\(\bf log_{\color{red}{ a}}{\color{red}{ a}}^x=x
\\ \quad \\ \quad \\
2^x=14\implies log_{\color{red}{ 2}}({\color{red}{ 2}}^x(=log_{\color{red}{ 2}}14\implies x=log_214\)

Answer 10

hmm \(\bf log_{\color{red}{ a}}{\color{red}{ a}}^x=x
\\ \quad \\ \quad \\
2^x=14\implies log_{\color{red}{ 2}}({\color{red}{ 2}}^x)=log_{\color{red}{ 2}}14\implies x=log_214\)

Answer 11

this makes sense to me. thank you for your help.