Question

express each of the following as a single log.
1. 2+ 3log base 10 x-2log base 10 y
2. 1+ log a -3log b
3. 3/2(log base 5 x-log base 5 y)

Answer 1

I'll try the first one then hopefully you'll be able to do the rest.
The second and third terms are already logs to base 10.
We need to express 2 as a log of a number (say y) to base 10.
2=log base10 y
Rewrite in exponent form
10^2=y
Thus y = 100, and therefore 2 = log base 10 100
The expression becomes
log base 10 100 + 3log base 10 x-2log base 10 y
Which can be written as
log base10 100 + log base10 x^3 - log base10 y^2
These combine into
log base10 ( (100*x^3)/(y^2) )