Duluan Mana?

Created by Ahmad Syahroni

we know that log (a x b)=log a + log b
then,the problem is in proving that log (a x b)=log a + log b
well,
let log a=n and log b=m
because of log a=log₁₀ a and log b=log₁₀ b
log₁₀ = 1

log a=n log b=m
a=10ⁿ ..........(1) b=10^m ............(2)

log (a x b)=log (10ⁿ x 10^m)
=log 10^n+m
=(n+m) log 10
=(n+m)
=log a + log b (it was proved)

then why log 10^n+m=(n+m) log 10 ?
or why log 10ⁿ=n log 10 ?
because log 10ⁿ =log (10x10x10x10x........x10) as much as n
=(log 10 + log 10 + log 10 +..........+ log 10) as much as n
=n log 10
then the problem is to prove log (a x b)=log a + log b we use the log 10^n+m=(n+m) log 10, but to prove log 10^n+m=(n+m) log 10, we use log (a x b)=log a + log b
so,which is the first formula?