Question 902106
Better notation in pure text:  5*log((x^3))-3*log((x^2))=12

With rendering tags,  {{{5*log((x^3))-3*log((x^2))=12}}}


Using logarithm rules and algebra,
{{{5*3*log((x))-2*3*log((x))=12}}}
Divide by 3.
{{{5*log((x))-2*log((x))=4}}}
{{{log((x^5))-log((x^2))=4}}}
{{{log((x^5/x^2))=4}}}
{{{log((x^3))=4}}}


But next, knowing which base is necessary.  Your exponential form for base b would be
{{{b^4=x^3}}}


Is b=10 for common logs?
{{{10000=x^3}}}
The easy way is cube root of 10000, {{{root(3,10000)}}}.
Would be {{{10*root(3,10)}}}.