Mathematics
If a = 1 + log 2 - log 5, b = 2 log 3, c = log P - log 5 and a + b = 2c, find the value of P.
Logarithms
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Answer
Given: a = 1 + log 2 - log 5, b = 2 log 3, c = log P - log 5
Now, a + b = 2c
⇒ (1 + log 2 - log 5) + 2 log 3 = 2 x (log P - log 5)
⇒ (log 10 + log 2 - log 5) + 2 log 3 = 2log P - 2log 5
⇒ log (2 x 5) + log 2 - log 5 + 2 log 3 = 2log P - 2log 5
⇒ log 2 + log 5 + log 2 - log 5 + 2 log 3 = 2log P - 2log 5
⇒ 2log P = 2log 2 + 2 log 3 + 2log 5
⇒ log P = log 2 + log 3 + log 5
⇒ log P = log (2 x 3 x 5)
⇒ log P = log 30
⇒ P = 30
Hence, the value of P = 30.
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