## anonymous one year ago 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

1. SolomonZelman

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

2. anonymous

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

3. SolomonZelman

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

4. SolomonZelman

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

5. SolomonZelman

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

6. anonymous

Oh no ;(. Really?

7. SolomonZelman

8. SolomonZelman

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

9. anonymous

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

10. anonymous

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

11. anonymous

Was that right?

12. SolomonZelman

yes, that was right

13. SolomonZelman

well done

14. anonymous

Yay! Thank you so much!!!