If log 7 - log 2 + log 16 - 2 log 3 - log = 1 + log k, find the value of k.

Question

KnowledgeBoat · Accepted Answer

⇒ log 7 - log 2 + log 16 - 2 log 3 - log = 1 + log k ⇒ log 7 - log 2 + log 24 - 2log 3 - (log 7 - log 45) = 1 + log k ⇒ log 7 - log 2 + 4log 2 - 2log 3 - log 7 + log 45 = 1 + log k ⇒ 3log 2 - 2log 3 + log (9 x 5) = 1 + log k ⇒ 3log 2 - 2log 3 + log 9 + log 5 = 1 + log k ⇒ 3log 2 - 2log 3 + log 32 + log 5 = 1 + log k ⇒ 3log 2 - 2log 3 + 2log 3 + log 5 = 1 + log k ⇒ 3log 2 + log 5 = log 10 + log k (∵ log 10 = 1) ⇒ 3log 2 + log 5 = log (2 x 5) + log k ⇒ 3log 2 + log 5 = log 2 + log 5 + log k ⇒ log k = 3log 2 + log 5 - log 2 - log 5 ⇒ log k = 2log 2 ⇒ log k = log 22 ⇒ log k = log 4 ⇒ k = 4 Hence, the value of k = 4.

Mathematics

If log 7 - log 2 + log 16 - 2 log 3 - log = 1 + log k, find the value of k.

Logarithms

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Mathematics

If log 7 - log 2 + log 16 - 2 log 3 - log = 1 + log k, find the value of k.

Logarithms

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