Question

simplify this natural log (: medal and fan

Answer 1

You can use the following rule for logs to solve this:
\[\ln a+\ln b=\ln ab\]

Answer 2

yeah so ln(4x^3*16x^2) right?

Answer 3

then take out the exponents?

Answer 4

Not really.
\[z=\ln (4x ^{3}+16x ^{2})+\ln (\frac{1}{5x ^{2}})=\ln [\frac{1}{5x ^{2}}(4x ^{3}+16x ^{2})]\ .........(1)\]
Can you now multiply out to remove the inner brackets?

Answer 5

yeah so = ln((4x+16)/5)

Answer 6

You are correct. Good work! Now we can simplify one step further by dividing each term in (4x + 16) by 5 to give decimal numbers.

Answer 7

what i initally did was try and solve the natural logs seperatly. i get it now, easy enough thnx

Answer 8

You're welcome :)