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!
<pre>{{{1/10 = (1/2)^(30/h)}}}
Since you want to use natural logs (ln), we then take the natural log of each side, as follows:
{{{ln (1/10) = ln (1/2)^(30/h)}}}
{{{ln (1/10) = (30/h) * ln (1/2)}}} ------- Applying {{{ln b^a}}} = {{{a * ln (b)}}}
{{{ln (1/10)/ln (1/2) = 30/h}}}
h = {{{30 * (ln (1/2)/ln (1/10))}}}
h = 9.03089987 &#8776; {{{highlight_green(9.03)}}}