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Given that log3(xy)=1 and \(\log_{3}(2x + y) = ...

Given that log3(xy)=1 and log3(2x+y)=2, find the value of x

A.

1

B.

2

C.

3

D.

4

Correct answer is D

log3(xy)=1xy=31=3....(1)

log3(2x+y)=22x+y=32=9.....(2)

From (1), y = x - 3

From (2), y = 9 - 2x

92x=x3

9+3=x+2x=3x

x=4