Logarithms and Their Properties?

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Logarithms and Their Properties?

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Answer 1 · 2018-07-10T13:54:49

$log 0.001 \sqrt[5]{p} = - 3 + \frac{1}{5} n$ $log 0.001 root (5)p=-3+1/5n$
$log (0.00001 \times \frac{p^{6}}{q^{7}}) = - 5 + 6 n + 7 m$ $log(0.00001times p^6/q^7)=-5+6n+7m$

Explanation:

If you just have plain "log", it means log base 10 ie ${log}_{10}$ $log_10$

$log 0.001 \sqrt[5]{p}$ $log 0.001 root (5)p$

Remember: $log a b = log a + log b$ $log ab=log a + log b$
= $log 0.001 + log \sqrt[5]{p}$ $log 0.001 + log root(5)p$

= ${log 10}^{- 3} + {log p}^{\frac{1}{5}}$ $log 10^(-3)+log p^(1/5)$

Remember: ${log}_{a} a = 1$ $log_a a=1$ and ${log}_{a} b^{n} = n {log}_{a} b$ $log_a b^n=n log_a b$ where n is a number
= $- 3 + \frac{1}{5} log p$ $-3+1/5log p$

= $- 3 + \frac{1}{5} n$ $-3+1/5n$

$log (0.00001 \times \frac{p^{6}}{q^{7}})$ $log(0.00001times p^6/q^7)$

Remember: $\frac{log a}{b} = log a - log b$ $log a/b= log a - log b$
= $log 0.00001 + {log p}^{6} + {log q}^{7}$ $log 0.00001 + log p^6 + log q^7$

= ${log 10}^{- 5} + {log p}^{6} + {log q}^{7}$ $log 10^(-5) + log p^6 + log q^7$

= $- 5 + 6 log p + 7 log q$ $-5+6log p+ 7 log q$

= $- 5 + 6 n + 7 m$ $-5+6n+7m$

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Logarithms and Their Properties?

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