Question

question
find the numerical value of the log expression.
$log a = -8$ $log b = -7$ $log c = 11$
$log \frac{sqrt{a^3}}{b^5 c^2}$

Explanation:

Step1: Rewrite root as exponent

$\log \frac{a^{\frac{3}{2}}}{b^5 c^2}$

Step2: Apply log quotient rule

$\log a^{\frac{3}{2}} - \log(b^5 c^2)$

Step3: Apply log product rule

$\log a^{\frac{3}{2}} - \log b^5 - \log c^2$

Step4: Apply log power rule

$\frac{3}{2}\log a - 5\log b - 2\log c$

Step5: Substitute given log values

$\frac{3}{2}(-8) - 5(-7) - 2(11)$

Step6: Calculate each term

$-12 + 35 - 22$

Step7: Compute final sum

$-12 + 35 = 23; 23 - 22 = 1$

Answer:

$1$