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Choose whether the given statement is true or false.
If , then we have to prove that

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True

False

answer is A.

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Detailed Solution

It is given that

. As the terms are equal, let each term be equal to k.

-----------------------(1.1)
Now, we know the logarithmic identity that

Therefore, using equations (1.1) and (1.2), we can obtain 3 equations as
Question Image

For the second term, we get
Question Image

For the third term, we get
Question Image

Also, we know that the logarithm of product of two numbers is given by

Therefore, as 12=3×4, we should have

Also, we can write

, therefore using the expression for logarithm of power from equation (1.2), we should have

Using this in equation (1.7), we get

Now, we can replace log (12), log(3), log(2) from equations (1.3), (1.4) and (1.5), we get
Question Image

Dividing log k on both sides, we obtain,
Question Image

From the above expression, we can say that we have proved what is asked.

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