Question

express as a single logrithm
6log(sub a)x+9log(sub a)y-5/3log(sub a)x

Answer 1

We know that\[\log_bx + \log_by = \log_b(xy)\]and\[\log_{b} x - \log_by = \log_b (\frac{ x }{ y } )\]

Answer 2

Applying those rules, we have\[\log_a x^6 + \log_a y^9 - \log_a x^{\frac{ 5 }{ 3 }}\]\[\log_a \left( \frac{ x^6 \times y^9 }{ x^{\frac{ 5 }{ 3 }}}\right) \rightarrow \log_a \left( x^{6-\frac{ 5 }{ 3 }}\times y^9\right)\]\[\log_a x^{\frac{ 13 }{ 3 }}.y^9 \rightarrow \log_a \sqrt[3]{x^{13}} .y^9\]