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If 10 0.3010 = 2, then find the value of log 0.125 125.?

Correct Answer: - 699 / 301

Explanation:

Exp. = log0.125125 = log2-3 53 = - 3/3log25 = -log25
∵ 100.3010 = 2
⇒ log102 = 0.3010
∵ log105 = log1010/2 = log1010-log102
= 1-0.3010 = 0.6990
∴ -log25 = - log105 / log102
= - 0.6990 / 0.3010 = - 699/301


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