What is the value of log3 log3 equal to?a)3 log2(3)b)1−3 log2(2)c)1−2 log3(2)d)Correct answer is option 'C'. Can you explain this answer?

Question

What is the value of log3 log3 equal to?a)3 log2(3)b)1&minus;3 log2(2)c)1&minus;2 log3(2)d)Correct answer is option 'C'. Can you explain this answer?

Answer

1. Product rule: The log of a product equals the sum of two logs.

⇒ log_a⁡(mn) = log_a⁡m+log_a⁡n

2. Quotient rule: The log of a quotient equals the difference of two logs.

⇒ log_a⁡

= log_a⁡m−log_a⁡n

3. Power rule: In the log of a power the exponent becomes a coefficient.

⇒ log_a⁡mⁿ= n log_a⁡m

4. Change of base rule:

⇒ log_m⁡n =

If m = n;

⇒log_m⁡m =

5. log_m⁡n =

Now,

Here, we have to find the value of log₃⁡log_3⁡

⇒ log₃⁡log₃

= log₃⁡log₃

⁡

= log₃⁡log₃

From power rule;

=log₃⁡[

×log₃⁡3][∵log_a⁡(m)n=n×log_a⁡(m)]

=log₃⁡

(∵logm⁡m=1)

=log₃⁡

= log₃⁡3−log₃⁡4

=1−log₃⁡4=1−log₃⁡22

=1−2log₃⁡(2)

Hence, the correct option is (C).

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