Log360=3log2+2log3+log5

Question

Assume base a=10

Answer 1

Using the properties of logarithms,  you can rewrite 360 as its "prime factorization"

360=2*2*2*3*3*5

 

With logarithms, log(a*b) = log(a) + log(b)

 

Also, log(aⁿ) = n*log(a)

 

 

log(360)=log(2*2*2*3*3*5)=

log(2)+log(2)+log(2)+log(3)+log(3)+log(5) =

3 log(2) + 2 log(3) + log(5)

Answer 2

Yes, it is true, based on rules of logarithms.

360 = 2³3²5 = 8(9)(5) = 72(5) = 360.

the log of a product is the sum of the logs of the factors;

the log of a power is the exponent times the log of the base.