Multiply the two results:4log25⋅5log36=625⋅36625⋅36=22500
Evaluate 2log9:9=32⟹log9=log(32)=2log3
So:
2log9=22log3=(2log3)2
Since 2log3=3, we get:
(2log3)2=32=9
Subtract the last term:22500−9=22491
Given the choices, it seems the problem may have intended different properties of logarithms or base conversions, but assuming the straightforward interpretation above:
22491
However, none of the provided options match this result. The provided answer choices might indicate a different expected approach, such as base manipulation or simplifications assumed in a different way. Double-check the problem context for further clues!
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Math Problem Analysis
Mathematical Concepts
Logarithms Exponents Properties of Logarithms Simplification
Formulas
a^log(b) = b^(log(a)) log(a^b) = b * log(a) Product and Power Rules of Exponents
Theorems
Change of Base Theorem Exponentiation and Logarithm Rules