Prove the second law of logarithms by using the law of exponents aˣ/aⁿ = aˣ⁻ⁿ
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Hi ,
Let a^x = p and a^n = q
a^x = p => log p ( base a ) = x
a^n = q => log q ( base a ) = n
p/q = a^x/a^n = a^x-n
Therefore ,
p/q = a^x-n
log ( p/q ) ( base a ) = x - n
Therefore ,
log (p/q)(base a)=log p(base a)-logq(base a)
I hope this helps you.
: )
Let a^x = p and a^n = q
a^x = p => log p ( base a ) = x
a^n = q => log q ( base a ) = n
p/q = a^x/a^n = a^x-n
Therefore ,
p/q = a^x-n
log ( p/q ) ( base a ) = x - n
Therefore ,
log (p/q)(base a)=log p(base a)-logq(base a)
I hope this helps you.
: )
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