Question

Given log2 a = x and log4 b = y then log2 (a³/b²) is equal to:
a) 3x + y
b) 3x + 4y
c) 3x - y
d) 3x - 4y

No idea how to do this one

Answer 1

b) 3x + 4y ..

Answer 2

how did you get that?

Answer 3

\[\log_2(\frac{a^3}{b^2})=\log_2(a^3)-\log_2(b^2)=3\log_2(a)-2\log_2(b)=3x-2\log_2(b)\]
Now that one part we have to think about
\[\log_4(b)=y => 4^y=b =>(2^2)^y=b => 2^{2y}=b => \log_2(b)=2y\]
So we have
\[\log_2(\frac{a^3}{b^2}) =3x-2 (2y)=3x-4y\]

Answer 4

Thank you so much!!