You have to know the logarithm rules and definition
Definition: if log(base a)x=b then x=a^b
Rules-I am going to use base 10 but it applies for every base:
4)change of base: loga=log(base b)a/log(baseb)10
So the first one I don't understand question.
Second: lnx=2 so x=e^2 (by definition)
Third: log(x+25)-log(2x-7)=1 so by using 3rd law: log[(x+25)/(2x-7)]=1 and then definition; 10^1= (x+25)/(2x-7) so cross multiplying; 10(2x-7)=x+25 so 20x-70=x+25 19x=95 x=5
Hope this helps