Base e- the natural logarithmic function

[adonai]

Write e[sup:2l6d44mb]ln[/sup:2l6d44mb][sup:2l6d44mb]8x^5-ln2x^2[/sup:2l6d44mb] as a single term that does not contain a logarithm. Show and explain all work.
I have this much done so far, and I am not certain that it is correct.
Because e[sup:2l6d44mb]ln x[/sup:2l6d44mb] =x, then e[sup:2l6d44mb]ln[/sup:2l6d44mb][sup:2l6d44mb]8x^5-ln2x^2[/sup:2l6d44mb] = 8x[sup:2l6d44mb]5[/sup:2l6d44mb]-2x[sup:2l6d44mb]2[/sup:2l6d44mb].

 

[tkhunny]

You are in the neighborhood, but you forgot your rules of logarithms.

\(\displaystyle e^{ln8x^{5}-ln2x^{2}} = e^{ln(8x^{5}/2x^{2})} = 8x^{5}/2x^{2} = 4x^{3}\)