Question

Help on logarithmic equations

Answer 1

 these logs are all base 6
logx-2log2=4log2

logx-log2^2=log2^4

log-log4=log16
logx/4=log16
x/4=16 (multiply by 4 to both sides)
x=64

Answer 2

$D:x\in\mathbb{R^+}\\\\use:\\log_ab-log_ac=log_a(\frac{b}{c})\\\\log_ab^c=c\cdot log_ab\\============================$

$log_6x-2log_62=4log_62\\\\log_6x-log_62^2=log_62^4\\\\log_6x-log_64=log_616\\\\log_6\frac{x}{4}=log_616\iff\frac{x}{4}=16\ \ \ \ |multiply\ both\ sides\ by\ 4\\\\\boxed{x=64}$