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.
