# How do you show that this statement is true log_16 2*log_2 16=1?

Nov 18, 2016

see explanation.

#### Explanation:

Using the $\textcolor{b l u e}{\text{laws of logarithms}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\log}_{b} x = n \Leftrightarrow x = {b}^{n}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {\log}_{16} 2 = n \Rightarrow 2 = {16}^{n} \Rightarrow n = \frac{1}{4}$

$\text{and } {\log}_{2} 16 = n \Rightarrow 16 = {2}^{n} \Rightarrow n = 4$

$\Rightarrow {\log}_{16} 2 \times {\log}_{2} 16 = \frac{1}{4} \times 4 = 1 \text{ hence True}$