Question

If log65 = 1.812 what is the value of log(base 1000)65 ? 0.0604 0.604 0.1812 0.001812

Answer 1

If we have:

logₐy = (logₓy) / (logₓa)       By change of base formula.

log₁₀65 = (log₁₀₀₀65) / (log₁₀₀₀10)

(log₁₀₀₀65)  = log₁₀65 * (log₁₀₀₀10)

log(₁₀₀₀10) =  1/ (log₁₀1000) = 1/(log₁₀10³) = 1/3

(log₁₀₀₀65)  = (log₁₀65) * (log₁₀₀₀10)

(log₁₀₀₀65)  = 1.812 * (1/3)       

(log₁₀₀₀65)  = 0.604

I hope this helps.