If log25 5 = a and log25 15 = b, then the value of log25 27 is

• Logarithms

If log₂₅ 5 = a and log₂₅ 15 = b, then the value of log₂₅ 27 is

1. 3(b+a)
2. 3(1-b-a)
3. 3(a+b-1)
4. 3(1-b+a)

Solution

a + b = log₂₅ 5 + log₂₅ 15 = log₂₅ 75 = log₂₅ 25 + log₂₅ 3

a + b = 1 + log₂₅ 3

a + b - 1 = log₂₅ 3

log₂₅ 27 = 3 log₂₅ 3 = 3(a + b - 1)

The correct option is C.