Question

HELP ME
5ln (x-1) =20

Answer 1

that 5 can be put up as the exponent...

(ln(x-1))^5 = 20

exponentiate..

e^(ln(1-x))^5 = e^20

(1-x)^5 = e^20

fifth root:

\[1-x = \sqrt[5]{e ^{20}}\]

subtract 1 from both sides and multiply by -1:

\[x = -\sqrt[5]{e ^{20}} +1\]

Answer 2

Divide both sides by 5:
ln(x-1) = 4
Raise both sides to the power e.
On the left e and ln will cancel out leaving with just (x-1)
x - 1 = e^4
add 1 to both sides.
x = e^4 + 1

Answer 3

so which on is correct?

Answer 4

one***

Answer 5

they are both right except I accidentally switched x-1 to 1-x in the middle of the problem.

So, my answer is actually:

\[x = \sqrt[5]{e ^{20}} + 1\]

Both give the same result though