Question

Given the exponential equation 2x = 128, what is the logarithmic form of the equation in base 10?

Answer 1

\(\Large 2^x = 128\)
Take logarithm to the base 10 on both sides. What do you get?

Answer 2

umm idk how do I find that?

Answer 3

\(\Large \log_{10}2^x = \log_{10}128\)
Use the logarithm property: \(\Large \log(a^n) = n * \log(a)\)

Answer 4

log base 10 of 2, all over log base 10 of 128 ?

Answer 5

\(\large 2^x = 128?\)

Answer 6

yes

Answer 7

\(\large \bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\

{\color{red}{ 2}}^x = {\color{blue}{ 128}}\implies ?\)

Answer 8

\(\Large \log_{10}2^x = \log_{10}128\)
\(\Large x\log_{10}2 = \log_{10}128\)

Answer 9

anyhow \(\bf log_{\color{red}{ a}}{\color{blue}{ b}}=y\implies {\color{red}{ a}}^y={\color{blue}{ b}}
\\ \quad \\ \quad \\

{\color{red}{ 2}}^x = {\color{blue}{ 128}}\implies log_{\color{red}{ 2}}{\color{blue}{ 128}}=x
\\ \quad \\
\textit{then you can just use the change of base rule }log_ab=\cfrac{log_{\color{olive}{ c}}b}{log_{\color{olive}{ c}}a}\)

for the log change of base rule, "c" can pretty much be anything, so long is the same atop and below

Answer 10

log_(2)128/log_(2)2?

Answer 11

well... you're expected to use log base10 though

Answer 12

Are you asked to solve for x or just write the logarithmic form of the equation to the base 10?

Answer 13

oh thank you haha yah so instead of 2 its ten

Answer 14

yeap

Answer 15

Ahhhh thankyou soo much!! This was corrrect ;)