Question

log 64 to the base 2√2

Answer 1

hope this helps......

Answer 2

Answer:

$log_{2\sqrt{2}}64= 4$

Step-by-step explanation:

$Let \: x = log_{2\sqrt{2}}64$

$\implies x = log_{2\times 2^{\frac{1}{2}}} 2^{6}$

$\implies x = log_{2^{\frac{(2+1)}{2}}}2^{6}$

$\implies x = log_{2^{\frac{(3)}{2}}} 2^{6}$

$\implies x = \frac{6}{\frac{3}{2}}\times log_{2}2$

\* we know the logarithmic law:

$\boxed {log_{a^{n}}a^{m} = \frac{m}{n}}$

$\implies x = 6 \times \frac{2}{3}$

$\implies x = 4$

•••♪