Question

If $\frac{3}{2}\log a+\frac{2}{3}\log b-1=0$, then the value of $a^9\cdot b^4$ is equal to

• A. ${10}^5$
• B. ${10}^6$
• C. ${10}^3$
• D. ${10}^7$

Answer 1

Answer: (B)

${10}^6$

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

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

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

$\therefore a^{\frac{3}{2}}\cdot b^{\frac{2}{3}}=10$
$\therefore a^9\cdot b^4={10}^6$