Answer to Question #271230 in Algebra for Gwappsg

Question

If log4 5=a and log5 6=b, then log3 2 is equal to

Answer 1

$a\cdot b=\log_45\cdot \log_56=\log_46=\frac{1}{2}\log_26=\frac{1}{2}(\log_23+\log_22)=\frac{1}{2}(\log_23+1)$

$2ab=\log_23+1$

$\log_23=2ab-1$

$\log_3 2=\frac{1}{\log_2 3}=\frac{1}{2ab-1}$

Answer: $\log_32=\frac{1}{2ab-1}$ .