Question 1018312
Find the EXACT solution to the equation below.
((log(x^3)+log(x^6))/log10x)=5

I tried solving it and I don't quite know if my answer is correct.

((log(x^3)+log(x^6))/log10x)=5

((x^3+x^6)/10x)=10^5
x^3+x^6-10x = 10^5
x^3+x^6-10x-10^5=0
<pre>Sorry, you're way off!!
{{{((log ((x^3)) + log ((x^6)))/log ((10x))) = 5}}}
{{{log ((x^3)) + log ((x^6)) = 5 * log ((10x))}}} ------------ Cross-multiplying
{{{log ((x^3)) + log ((x^6)) = 5 * (log ((10)) + log ((x)))}}} --- Applying {{{log ((ab))}}} = {{{log ((a)) + log ((b))}}}
{{{log ((x^3)) + log ((x^6)) = 5 * (1 + log ((x)))}}}
{{{log ((x^3)) + log ((x^6)) = 5 + 5 * log ((x)))}}}
{{{log ((x^3)) + log ((x^6)) - 5 * log ((x)) = 5}}}
{{{log ((x^3)) + log ((x^6)) - log ((x^5)) = 5}}}
{{{log ((x^3 * x^6)/x^5) = 5}}} ----> {{{log ((x^9)/x^5) = 5}}} -----> {{{log ((x^4)) = 5}}} -----> {{{4 * log ((x)) = 5}}} -----> {{{log ((x)) = 5/4}}} -----> {{{highlight(highlight_green(highlight(x = 10^(5/4))))}}}