Question 89
The value of $$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$ is equal to
Solution
$$\log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7$$
$$81 = 3^4$$ and $$0.008 = \frac{8}{1000} = \frac{2^{3}}{10^{3}} = \frac{1}{5^{3}} = 5^{-3} $$
Hence,
$$\log_{0.008}\sqrt{5}+ 8 -7 $$
$$ \log_{5^{-3}}5^{\frac{1}{2}}+ 8 -7 $$
$$\frac{log 5^{0.5}}{log 5^{-3}} + 1$$
$$ - \frac{1}{6} + 1$$
= $$\frac{5}{6}$$
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