Question

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

Explanation:

Step1: Apply log quotient rule

$\log \frac{b^7}{a^3c^8} = \log b^7 - \log(a^3c^8)$

Step2: Apply log product rule

$\log b^7 - \log(a^3c^8) = \log b^7 - (\log a^3 + \log c^8)$

Step3: Apply log power rule

$\log b^7 - \log a^3 - \log c^8 = 7\log b - 3\log a - 8\log c$

Step4: Substitute given values

$7(-11) - 3(-11) - 8(5)$

Step5: Calculate each term

$-77 + 33 - 40$

Step6: Compute final sum

$-77 + 33 = -44; -44 - 40 = -84$

Answer:

$-84$