Question Details

Suppose, log3 x = log12 y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log6 G is equal to

Options

A

√a

B

2a

C

a/2

D

a

Show Answer

Correct Answer :

Option D

a

Solution :

Correct Option: D

We are given:
log3x=ax=3a
log12y=ay=12a

Since G is the geometric mean of x and y, we have:
G=xy
Substituting the values of x and y:
G=3a·12a=(3·12)a=36a=(62)a2=6a

Now, we need to find log6G:
log6G=log6(6a)=a

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