Question

Evaluate the following

Log₃⁸¹

Log₂₇³

Log₆₄⁴

Log₉₀¹

1Log

Answer 1

There are some useful properties of logarithms that we will use: $\log_{a^k}a = \frac{1}{k}$ , $\log_{a}a^m = m$, $\log_a1=0$.

$\displaystyle \log_381=\log_3 3^4=4$

$\displaystyle \log_{27}3 = \log_{3^3}3=\frac{1}{3}$

$\displaystyle \log_{64} 4 = \log_{4^3}4= \frac{1}{3}$

$\log_{90}1=0$