Question

Log (10)25+log (10)4=log (5)25

Answer 1

$\text{consider,}$

$log_{10}25+log_{10}4$

$\text{Using, product rule of logarithm }$

$\boxed{\bf\log_aM+log_aN=log_aM\,N}$

$=log_{10}(25{\times}4)$

$=log_{10}100$

$=log_{10}10^2$

$\text{Using, power rule of logarithm }$

$\boxed{\bf\log_aM^n=n\,log_aM}$

$=2\log_{10}10$

$\text{Using, \bf\,log_{a}a=1 }$

$=2(1)$

$=2\,log_{5}5$

$=log_{5}5^2$

$=log_{5}25$

$\implies\boxed{\bf\,log_{10}25+log_{10}4=log_{5}25}$

Answer 2

L.H.S; I RHS;

Log(10)25+Log(10)4. I Log(5)(25)

=Log(10)(25x4) I =Log(5)(5)^2

=Log(10)(100) I =2 Log (5)5

=Log(10)(10)^2. I =2

=2 Log (10)10. I

=2

L.H.S=R.H.S

PROVED;

Hope it helps.