Question 1204581
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For simplicity, we can ignore the log base 7 and consider the same expression in standard base 10 logarithms.<br>
{{{log((root(3,x)))-log((y^3))+2log((y))}}}<br>
Write the expression as a single logarithm using 3 basic log rules:
(1) {{{a*log((b))=log((b^a))}}}
(2) {{{log((a))-log((b))=log((a/b))}}}
(3) {{{log((a))+log((b))=log((ab))}}}<br>
Use (1) to write {{{2log((y))}}} as {{{log((y^2))}}}<br>
{{{log((root(3,x)))-log((y^3))+log((y^2))}}}<br>
Then use (2) and (3).  The "- log" becomes a division and the "+ log" becomes a multiplication:<br>
{{{log(((root(3,x))/y^3*y^2))}}}<br>
Then simplify to get the final result.<br>
{{{log(((root(3,x))/y))}}}<br>