Asked by tor
Approximate the following logarithms using the properties of logarithms given
logb(2)=0.264,
logb(3)=0.419,
and
logb(5)=0.614.
logb(24) =?
logb(100) =?
logb(5b^3) =?
logb(2)=0.264,
logb(3)=0.419,
and
logb(5)=0.614.
logb(24) =?
logb(100) =?
logb(5b^3) =?
Answers
Answered by
Steve
assuming logs base b, we have
log(24) = log(2^3 * 3) = 3log2+log3 = 3*0.264 + 0.419 = 1.211
log(100) = log(10^2) = 2log10 = 2log(2*5) = 2(log2+log5) = ...
log(5b^3) = log5 + 3logb = 0.614 + 3 = 3.614
since logb(b) = 1
log(24) = log(2^3 * 3) = 3log2+log3 = 3*0.264 + 0.419 = 1.211
log(100) = log(10^2) = 2log10 = 2log(2*5) = 2(log2+log5) = ...
log(5b^3) = log5 + 3logb = 0.614 + 3 = 3.614
since logb(b) = 1