Mathematics
Consider the following two statements :
Statement 1: log5 150 = log5 25 + log5 125
Statement 2: loga (b + c) = loga b + loga c
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Logarithms
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Answer
According to statement 1; log5 150 = log5 25 + log5 125
Solving R.H.S.,
⇒ log5 25 + log5 125
⇒ log5 (25 x 125)
⇒ log5 3125.
As, log5 150 ≠ log5 3125
∴ Statement 1 is false.
According to statement 2; loga (b + c) = loga b + loga c
Solving R.H.S.
⇒ loga b + loga c
⇒ loga (b x c)
⇒ loga bc.
As, loga (b + c) ≠ loga bc
∴ Statement 2 is false.
∴ Both statements are false.
Hence, option 2 is the correct option.
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