Question

\[\log_{a}(x/y)=4.5\] and \[\log_{a}x^{5}y^{2}=5\], find the value of \[\log_{a}\sqrt{xy}\] heeeeeeeeelp........

Answer 1

:'D JOEMATH~ <3

Answer 2

its a system of equations.\[\log_a\left(\frac{x}{y}\right)=\log_ax-\log_ay\]\[\log_ax^5y^2=5\log_ax+2\log_ay\]\[\log_a\sqrt{xy}=\frac{1}{2}\log_ax+\frac{1}{2}\log_ay\]
Let:\[f=\log_ax,g=\log_ay\]basically you are solving the system of equations:\[f-g=4.5\]\[5f+2g=5\] which is two equations and 2 unknowns, solve however you please. Then once you get f and g, your answer will be:\[\frac{1}{2}f+\frac{1}{2}g\]

Answer 3

I'm lost at solving D:
f=2
g=-2.5
............what do you do with that?

Answer 4

Look at Joe's 3rd equation. remember what f and g stand for?

Answer 5

OMG I LOVE YOU GUYS <3

Answer 6

I never look back on an equation I just move on and get stuck :p thanks

Answer 7

-0.25 :DDDDDDDDDDDDDD

Answer 8

God I'm so slow.