Hi;
log_{2}x=p and log_{4}y=q
We have a log to the base of 2.
We have a log to the base of 4.
We would like each to be of the same base.
I choose base of 2. You will understand why below.
log_{4}y=(log_{2}y)/(log_{2}4)
log_{2}4=2 because 2^{2}=4
log_{2}y/2
(1/2)log_{2}y
log_{2}x=p and (1/2)log_{2}y=q
x^{2}y
log ab=log a+log b
log_{2}x^{2}y=log_{2}x^{2}+log_{2}y
log_{2}x^{2}y=2log_{2}x+log_{2}y
Let's multiply both sides by (1/2)
(1/2)log_{2}x^{2}y=log_{2}x+[(1/2)log_{2}y]
(1/2)log_{2}x^{2}y=p+q
Let's multiply both sides by 2...
log_{2}x^{2}y=2p+2q
Let's move the base of 2 over to the right side...
x^{2}y=2^{2p+2q}
Feb 8

Vivian L.
Comments
How did I do?