SOLUTION: I am particular to doing the e^ln to each side of a number. And this problem is troublesome. I want to find the answer to: 1/10 = (1/2)^(30/h) I keep running into problem

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Question 999930: I am particular to doing the e^ln to each side of a number. And this problem is troublesome.
I want to find the answer to:
1/10 = (1/2)^(30/h)
I keep running into problems, since there is an exponential on one side, I take the e to the ln of each side like so:
e^ln(1/10) = e^(ln(1/2)^(30/h))
e^ln(1/10) = e^((30/h)ln(1/2))
Then since anything to the e^ln cancels for both sides:
1/10 = (30/h)(1/2)
Something doesn't smell right here. What did I do wrong and how can I get the correct answer of h = 9.03
Thank you!
Found 2 solutions by fractalier, MathTherapy:
Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website!
Okay, from
1/10 = (1/2)^(30/h)
you just take the ln first...
ln(1/10) = ln[(1/2)^(30/h)]
ln(1/10) = (30/h)ln(1/2)
since ln(1/x) = -ln x, we get
-ln10 = (30/h)(-ln2)
and
30/h = -ln10/-ln2 = ln10/ln2
and rearranging gives
h = 30/(ln10/ln2) = 30 ln 2 / ln 10 = 9.03

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
I am particular to doing the e^ln to each side of a number. And this problem is troublesome.
I want to find the answer to:
1/10 = (1/2)^(30/h)
I keep running into problems, since there is an exponential on one side, I take the e to the ln of each side like so:
e^ln(1/10) = e^(ln(1/2)^(30/h))
e^ln(1/10) = e^((30/h)ln(1/2))
Then since anything to the e^ln cancels for both sides:
1/10 = (30/h)(1/2)
Something doesn't smell right here. What did I do wrong and how can I get the correct answer of h = 9.03
Thank you!

Since you want to use natural logs (ln), we then take the natural log of each side, as follows:

------- Applying =

h =
h = 9.03089987 ≈