Question

Given log5 3=0.6826 and log5 8=1.2920, evaluate the expressions

Please help!?

Answer 1

a) 1.3652

b) 1.3906

Explanation:

a) log5 9 = log5 3² = 2log5 3 = 2(0.6826) = 1.3652

b) log5 75/8 = log5 75 - log5 8 = log5 3×25 - log5 8=

log5 3 + log5 5² - log5 8 = 0.6826 + 2 - 1.2920 = 0.6826 + 0.708 = 1.3906

Answer 2

`\begin{array}{llll} \textit{Logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of rationals} \\\\ \log_a\left( (x)/(y)\right)\implies \log_a(x)-\log_a(y) \end{array} \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\log_5(9)\implies \log_5(3^2)\implies 2\log(3)\implies 2(0.6826)~~ \approx~~1.3652 \\\\[-0.35em] ~\dotfill\\\\ \log_5\left( \cfrac{75}{8} \right)\implies \log_5(75)~~ - ~~\log_5(8)\implies \log_5\left( \cfrac{75}{8} \right) \\\\\\ \log_5(3\cdot 5^2)~~ - ~~\log_5(8)\implies [\log_5(3)~~ + ~~\log_5(5^2)]~~ - ~~\log_5(8) \\\\\\ \log_5(3)~~ + ~~2\log_5(5)~~ - ~~\log_5(8) \\\\\\ 0.6826~~ + ~~2~~ - ~~1.2920\implies 1.3906`