Question 1105687
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Thanks for taking the time to try to help your daughter....<br>
x and v are variables; you won't get a numerical answer to the problem; you will get an answer involving x and v.<br>
When a problem involving logarithms does not specify the base, it is assumed that the base is 10.  However, in this problem we are working with variables instead of numbers; so the base is irrelevant -- the problem could be in any base.<br>
A logarithm is an exponent, so the laws for dealing with logarithms are essentially the same as the laws for dealing with exponents.  Specifically,<br>
(1) {{{log((a*b)) = log((a))+log((b))}}}
(2) {{{log((a/b)) = log((a))-log((b))}}}
(3) {{{log((a^b)) = b*log((a))}}}<br>
I believe the expression you are given is
{{{(1/3)log((x)) - 3log((v))}}}<br>
Using the basic laws of logarithms...
{{{(1/3)log((x)) = log((x^(1/3)))}}}  [rule (3)]
{{{3log((v)) = log((v^3))}}}  [rule (3)]
{{{(1/3)log((x)) - 3log((v)) = log((x^(1/3))) - log((v^3)) = log((x^(1/3)/v^3))}}}<br>  [rule (2)]
So {{{a = x^(1/3)/v^3}}}