Given that log base of 2 3=x,log base of 2 5=y and log base of 2 7=z what is log base of 2 15/7 in terms of...

..in terms of x,y,and z?
a.2^x times 2^y divided by 2^z
b.x+y-z
c.xy/z
d.1+x-z

ans is b) x+y-z

_2 refers to base 2

x+y-z = log_2 (3) + log_2(5) - log_2(7)

= log_2( 15) - log_2(7)
= log_2 (15/7)

given that log base of 2 3=x,log base of 2 5=y and log base of 2 7=z what is log base of 2 15/7 in terms of...?

..in terms of x,y,and z?
Sol log base of 2 3=x,log base of 2 5=y and log base of 2 7=z
3 = 2^x........................(i)
5 = 2^y......................(ii)
7 = 2^z...................(iii)
15/7 = 3*5/7 = 2^x*2^y/2^z = 2^(x+y-z)............Ans (a)

a.(2^x)(2^y)/(2^z) = 2^(x+y-z)..................Ans
b.x+y-z
c.xy/z
d.1+x-z