Which of the following equations is equivalent to
y = lnx?

A. x = y^e
B. y = x^e
C. y = e^y
D. y = e^x

Question

Which of the following equations is equivalent to
y = lnx?

A. x = y^e
B. y = x^e
C. y = e^y
D. y = e^x

solomonzelman · Answer

$\large\ln(x)$   is  same  as  $\large\log_{e}(x)$

anonymous · Answer

Ok ok, so would I take the 'e' and sort of "bump" it over to the 'y' slot making e^y?

solomonzelman · Answer

$\large\color{black}{ \displaystyle y=\ln(x) }$

$\large\color{black}{ \displaystyle y=\log_{e}(x) }$

then apply the rule:

$\huge\color{black}{ \displaystyle \color{red}{\rm a}=\log_{\color{green}{\rm b}}(\color{blue}{\rm c})~~~~~\Longrightarrow ~~~~~ \displaystyle \color{green}{\rm b}^{\color{red}{\rm a}}=\color{blue}{\rm c}  }$

solomonzelman · Answer

this rule that I drew with many colors, is what you should use for your final answer.

solomonzelman · Answer

actually, the way you wrote the options, none of them are correct-;(

anonymous · Answer

Oh no ;(. Really?

solomonzelman · Answer

you made a typo in your options. check them

solomonzelman · Answer

but, do it without options and tell me what you get

anonymous · Answer

I would first set it as $$y = \log_{e} x$$ and then turn it into $$e ^{y} = x$$

anonymous · Answer

Oh and option C should be x=e^y. Sorry

anonymous · Answer

Was that right?

solomonzelman · Answer

yes, that was right

solomonzelman · Answer

well done

anonymous · Answer

Yay! Thank you so much!!!