Change-of-Base Formula

[nycmathguy]

Section 3.3
10 & 12

Question 10

log 12/log 0.4 = -2.7119194414

Answer: -2.712

Question 12

log 0.125/log (2/3) = 5.1285338747

Answer: 5.129

 

[MathLover1]

correct
but, you need to do steps

log(0.4,12) ->to base 10
log(12)/log(0.4)..............write 12 as 3*4 and 0.4 as 4/10

log(3*4)/log(4/10)

apply log rules: log(xy)=log(x)+log(y) and log(x/y)=log(x)-log(y)

(log(3)+log(4))/(log(4)-log(10)).......log(10)=1 and log(4)=log(2^2)=2log(2)
(log(3)+2log(2))/(2log(2)-1)=-2.7119194414

 

[nycmathguy]

correct
but, you need to do steps

log(0.4,12) ->to base 10
log(12)/log(0.4)..............write 12 as 3*4 and 0.4 as 4/10

log(3*4)/log(4/10)

apply log rules: log(xy)=log(x)+log(y) and log(x/y)=log(x)-log(y)

(log(3)+log(4))/(log(4)-log(10)).......log(10)=1 and log(4)=log(2^2)=2log(2)
(log(3)+2log(2))/(2log(2)-1)=-2.7119194414

I get it. Steps have to be shown along the way.