The final value of the given log expression is -28
Logarithm functions
Logarithm functions are inverse of exponential functions. Given the log expression below;
[tex]log\frac{c^5}{\sqrt{b^3}}[/tex]
Given the following parameters
log a = 6
log b = -10
log c = -8
The log expression can be expressed as:
[tex]log\frac{c^5}{\sqrt{b^3}}=logc^5-log(\sqrt{ab^3})\\log\frac{c^5}{\sqrt{b^3}}=5logc-(1/2loga +3/2logb)\\log\frac{c^5}{\sqrt{b^3}}=5(-8)-(1/2(6)+3/2(-10))\\log\frac{c^5}{\sqrt{b^3}}=-40-(3-15)\\log\frac{c^5}{\sqrt{b^3}}=-40+12\\log\frac{c^5}{\sqrt{b^3}}=-28[/tex]
Hence the final value of the given log expression is -28
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