Question

3 = log8 + 3logx. help me please

Answer 1

$The\ domain:\\D:x \ \textgreater \ 0\\\\\log8+3\log x=3\\\\use:\\a\log b=\log b^a\\ \log a+\log b=\log(a\cdot b)\\\log_ab=c\iff a^c=b\\\\\log8+\log x^3=\log10^3\\\\\log8x^3=\log10^3\iff8x^3=1000\ \ \ \ |divide\ both\ sides\ by\ 8\\\\x^3=125\to x=\sqrt[3]{125}\to\boxed{x=5}\in D$