Question

show that, log 2 to the base 4 * log 3 to the base 2= log 5 to the base 4 * log 3 to the base 5​

Answer 1

FORMULA

$log_{b}(a)=\frac{ log(a) }{ log(b) }$

PROOF

LHS

$= log_{4}(2) \times log_{2}(3)$

$= \frac{ log(2) }{ log(4) } . \frac{ log(3) }{ log(2) }$

$= \frac{ log(3) }{ log(4) }$

$= log_{4}(3)$

RHS =

$log_{4}(5) \times log_{5}(3)$

$= \frac{ log(5) }{ log(4) } . \frac{ log(3) }{ log(5) }$

$= \frac{ log(3) }{ log(4) }$

$= log_{4}(3)$

LHS = RHS, Hence Proved.