Question

Please help me find x for the following (click to see equation).

Answer 1

\[2e^x-1=0\]

Answer 2

\[2e^x=1\]

Answer 3

\[e^x=1/2\]

Answer 4

Now, how do I find x?

Answer 5

take the natural log of both sides. ln(e^x) is just x

Answer 6

\[\ln(e^x)=\ln(1/2)\]

Answer 7

\[x=\ln(1/2)\]

Answer 8

yes

Answer 9

the correct answer in the book is -ln2

Answer 10

i understand it is the same value...

Answer 11

But I am using the x value is a critical value to find the relative extrema of a function, does it matter if I use ln(1/2) or -ln2?

Answer 12

as* a critical value

Answer 13

@Algebraic!

Answer 14

yeah, same thing: ln(1/2) = ln (2^-1) = - ln(2)
all different ways of expressing the same thing. check with your calculator if you like..

Answer 15

"But I am using the x value is a critical value to find the relative extrema of a function, does it matter if I use ln(1/2) or -ln2?"

no, they are all exactly the same number.

Answer 16

ok thanks