Question

If $\frac{3}{2}\log a+\frac{2}{3}\log b-1=0$, find the value of $a^9{b}^4$.

Answer 1

Given that,

$\frac{3}{2}\log a+\frac{2}{3}\log b-1=0$

$\log (a{)}^{\frac{3}{2}}+\log (b{)}^{\frac{2}{3}}=1$

$\log \left(a{)}^{\frac{3}{2}}\right(b{)}^{\frac{2}{3}}=1$

$\log \left(a{)}^{\frac{9}{6}}\right(b{)}^{\frac{4}{6}}=1$

$(a^9{b}^4{)}^{\frac{1}{6}}={10}^1=10$

$\therefore a^9{b}^4={10}^6$