1. ## Exponents and log

x3/2 = 27/64, so x = ¾ and ln(12 + x) = (ln 12)(ln x)

2. $\displaystyle x^{\frac{3}{2}}= \frac{27}{64}$

$\displaystyle (\sqrt{x})^3= \frac{27}{64}$

$\displaystyle \sqrt{x}= \frac{3}{4}$

$\displaystyle x= \frac{9}{16}$

3. You have ln(12+x)=ln12+lnx Therefore ln(12+x)=ln12x if you put e to both logs you get 12+x=12x---->12=11x--->x=12/11

I would normally be more wordy and explain each step but I see they don't do that here.

.....I was given these problems to fix the errors!
ln(12 + x) = (ln 12)(ln x)
Assuming this is an error?

It should be

$\ln a +\ln b = \ln (a\times b)$

5. Yes I was given both of those equations to find the errors.

6. Thank you everyone!