Question

найти log (36) 9 если log(36)8=m

Answer 1

$m=log_{36}8=log_{6^2}2^3=\frac{3}{2}\, log_62\; \; \to \; \; \; log_62=\frac{2m}{3}\\\\log_62=\frac{1}{log_26}=\frac{2m}{3}\; \; \; \to \; \; \underline {log_26=\frac{3}{2m}}\\\\\\log_26=log_2(2\cdot 3)=log_22+log_23=1+log_23=\frac{3}{2m}\; \; \to \\\\log_23=\frac{3}{2m}-1\; \; \; \to \; \; \; \underline {log_23=\frac{3-2m}{2m}}\\\\\\log_{36}9=log_{6^2}\, 3^2=log_63=\frac{log_23}{log_26}=\frac{3-2m}{2m\cdot \frac{3}{2m}}=\frac{3-2m}{3}\\\\\boxed{log_{36}9= \frac{3-2m}{3}}$