Answer to Question #271230 in Algebra for Gwappsg

Question #271230

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


1
Expert's answer
2021-11-25T16:15:26-0500

ab=log45log56=log46=12log26=12(log23+log22)=12(log23+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=log23+12ab=\log_23+1

log23=2ab1\log_23=2ab-1

log32=1log23=12ab1\log_3 2=\frac{1}{\log_2 3}=\frac{1}{2ab-1}


Answer: log32=12ab1\log_32=\frac{1}{2ab-1} .


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