Additional Mathematics – Logarithmic and exponential functions | e-Consult
Logarithmic and exponential functions (1 questions)
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log5 125 = \(\dfrac{\ln 125}{\ln 5}\) (change of base).
Since 125 = 5³, \(\ln 125 = \ln(5³) = 3\ln 5\).
Thus \(\dfrac{\ln 125}{\ln 5} = \dfrac{3\ln 5}{\ln 5} = \mathbf{3}\).