Question

Simplify into a single Logarithm. Log (base4)18 – (0.5 log (base4) 36+2log (base4)3)

Answer 1

$log_4 18-0.5\ log_436+2\ log_43$

$=log_4 18- log_4(36)^{0.5}+log_43^2\\ \\=log_4 18- log_46+2\ log_49\\ \\=log_4( \frac{18 \times9}{6} )\\ \\ =log_427$

Answer 2

$log_{4}18 - (0.5) log_{4}36 + 2 log_{4}3$

$log_{4}18 - log_{4} \sqrt{36} + log_{4}9        [ mloga = loga^m]$

$log_{4} \frac{18*9}{6}$

$log_{4}27$