Question

If $\log (a{)}^3+\log a$ = $m\log a$, then value of $m$ is equal to

• A. $1$
• B. $4$
• C. $2$
• D. $-5$

Answer 1

The correct option is B $4$

According to Logarithm power rule,
${\log }_b\left(X^Y\right)=Y.{\log }_b\left(X\right)$
Therefore, $\log (a{)}^3=3.\log a$
Since, $\log (a{)}^3+\log a=m\log a$
Therefore, $3.\log a+\log a=m\log a$
$4.\log a=m\log a$
By comparing both the sides we get,
$m=4$
Hence, option B is correct.