Question

Solve for x and y; if x>0 and y>0:
log xy=log x÷y+ 2log2=2

Answer 1

We can solve the given question as follows:

Given, log(xy) = 2 −−−−(i)

log(x/y) + 2 log(2) = 2 −−−−(ii)
From (i), we get:
log(x) + log(y) = 2 −−−−−−(iii)
From (ii), we get:
log(x) − log(y) = 2 − 2 log(2) −−−−−(iv)

Adding (iii) and (iv), we get:So,
2 log(x) = 2( 2 − log(2))
or, log(x) = 2 − log(2)
or, log(x) + log(2) = 2
or, log(2x) = 2
Taking inverse log on both the sides, we get:
2x = e^2
x= e^2/2

Subtracting (iv) from (iii), we get2 log y = 2 log 2
⇒log y^2 = log 2^2
⇒y^2 = 4
⇒y = 2