# Help with this sample proble for college entrance exam!!

• Mar 31st 2011, 10:13 PM
jessmari86
Help with this sample proble for college entrance exam!!
Hi need help understanding how to simplify this expression with steps i do not know how these online math solvers got their answers.
sqrt= square route ^means to the 1/3 power just in case you were confused.
expression:

4ln(sqrt(x))+6ln(x^(1/3))

math solver got ln(x^4)

any help will be appriciated thanks
• Mar 31st 2011, 10:16 PM
Prove It
You need to make use of the formulas

$\displaystyle n\log{(x)} = \log{\left(x^n\right)}$ and $\displaystyle \log{(a)} + \log{(b)} = \log{(ab)}$.
• Mar 31st 2011, 10:49 PM
jessmari86
ok so how does that apply here i already got that the 6ln(x^(1/3))=2ln(x) right?? and i look for examples for a problem with the sqrt but cannot find any its been like 8 or 9 years sincer i was last using math like this. how would i simplify the 4ln(sqrt(x))???
• Mar 31st 2011, 11:02 PM
jessmari86
ohhhhhhhhhhhhhhhhhhh i think i got it so heres what i got for showing my work let me know

4ln(sqrt(x))+6ln(x^(1/3))------------------>square the 4, and divide the 6 by 3 to isolate the x's
2ln(x) + 2ln(x)
4ln(x)----------------> using that rule n log(x) = log(x^n) thus getting the

ln(x^4)
• Mar 31st 2011, 11:06 PM
Prove It
You actually halve the 4, but yes, you have the general idea. Well done.