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

a. x = e^y
b. y = e^x
c. y = x^e
d. x = y^e

Question

Which of the following equations is equivalent to y = lnx ?

a. x = e^y
b. y = e^x
c. y = x^e
d. x = y^e

bibby · Answer

Remember the property of logs. (natural logs anyways)

a = e^b
if you take the ln of both sides of that, you end up with

ln(a) = b*ln(e)

anonymous · Answer

huh?

bibby · Answer

whoops misread the question.

what is ln(e^x)?

anonymous · Answer

I dont understand

bibby · Answer

Then go learn the properties of natural log and come back.

anonymous · Answer

Take the ln of each of the answers and one will be what you seek.

bibby · Answer

the third property in this image in particular

anonymous · Answer

is it d?

solomonzelman · Answer

the first question you asked.

 y = lnx ?

a. x = e^y
b. y = e^x
c. y = x^e
d. x = y^e

$$y=lnx~~~~~~~~~->~~~~~~y=\log_ex.$$$$formula:~~~~~~~~~\log_ab=c~~~~~~->~~~~~~a^c=b$$

anonymous · Answer

so you're saying it's y = e^x ?

bibby · Answer

if you take the ln of both sides of that you get ln y = x ln e
and ln e simplifies to 1.

anonymous · Answer

where did the e come from?

anonymous · Answer

try taking the ln of both sides of a)

bibby · Answer

y = e^x ?
ln(y) = ln(e^x)

anonymous · Answer

okay

solomonzelman · Answer

$$\ln~(anything)=\log_e(anything)$$

bibby · Answer

she's clearly interested in learning about the math behind this

solomonzelman · Answer

yes, I see this.

solomonzelman · Answer

y = lnx
is just saying the same thing as
 y = log(base e) x

and you were right, it is e^y=x