The value of log 0.008 √5 + log √3 81 – 7 is equal to:

Question

The value of log 0.008 &radic;5 + log &radic;3 81 &ndash; 7 is equal to:

Accepted Answer

5/6 — Easy Rewrite each base and argument as a power of a single prime, then use $\log_{p^m}p^n=	frac{n}{m}$. Evaluate the two log terms separately and combine with the $-7$. 1 First term. Note $0.008=	frac{8}{1000}=	frac{1}{125}=5^{-3}$ and $\sqrt5=5^{1/2}$: $$\begin{aligned} &\log_{0.008}\sqrt5=\log_{5^{-3}}5^{1/2}=\frac{1/2}{-3}=-\frac{1}{6} \end{aligned}$$ 2 Second term. $\sqrt3=3^{1/2}$ and $81=3^4$: $$\begin{aligned} &\log_{\sqrt3}81=\log_{3^{1/2}}3^{4}=\frac{4}{1/2}=8 \end{aligned}$$ 3 Combi

CAT 2017 Slot 1 — QA Question 23

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