If log102 = p and log103 = q, the value of log12536 is equal to which of the following?
Question
If log10 2 = p and log10 3 = q, the value of log10 2536 is equal to which of the following?
Solution
The given question is a logarithmic problem. Here's how you can solve it:
First, we need to express the number 12536 in terms of 2 and 3. The prime factorization of 12536 is 2^4 * 3^4 * 7^2.
So, log10(12536) can be written as log10(2^4 * 3^4 * 7^2).
Using the properties of logarithms, this can be further simplified to 4log10(2) + 4log10(3) + 2*log10(7).
We know from the problem that log10(2) = p and log10(3) = q. Substituting these values, we get 4p + 4q + 2*log10(7).
So, the value of log10(12536) is equal to 4p + 4q + 2*log10(7).
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