Question

If log_10(2)=x and log_10(3)=y, then what is the value of log_10(15) in terms of x and y?

*the first logarithmic equation reads: the logarithm of x with base 10 is is 2.

Answer 1

log_10(15)=log(15)/log(10)
log(10)=1
log(10)=log(5*2)=log(5)+log(2)=1
log(2)=x
so replacing it is log(5)=1-x
then in the first part
log(15)=log(3*5)=log(3)+log(5)=y+1-x
so log_(10)=log(15)/log(10)=y+1-x/1
so finally it equals log_10(15)=y+1-x

hope you understand my solution, I didn't put the base 10 in some parts of the exercise because it is understandable

Answer 2

or

15 = (10x3÷2)
take log of both sides

log 15 = log (10x3÷2)
= log10 + log3 - log2
= 1 + y - x