Prove Change-of-Base Formula

[nycmathguy]

 

[MathLover1]

prove
log(a,x)=log(b,x)/log(b,a)

first
Let log(a, x)=y

then write in exponent form
a^y = x

then take log (base b ) of both sides and evaluate

log(b, a^y) = log (b, x)
y*log(b, a) = log (b, x)........substitute y

log(a, x)*log(b, a) = log (b, x)
log(a, x)= log (b, x)/log(b, a)

 

[nycmathguy]

prove
log(a,x)=log(b,x)/log(b,a)

first
Let log(a, x)=y

then write in exponent form
a^y = x

then take log (base b ) of both sides and evaluate

log(b, a^y) = log (b, x)
y*log(b, a) = log (b, x)........substitute y

log(a, x)*log(b, a) = log (b, x)
log(a, x)= log (b, x)/log(b, a)

What can I say? You are a true mathematician. You are someone I hope to be before my time on earth comes to an end.