MATHEMATICS

JAMB 2022 - Question 22

Mathematics 2022 JAMB Past Questions - Question 22: Simplify 2log2/5 – log72/125 + log9

Simplify 2log2/5 – log72/125 + log9
A:
B:
C:
D:
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Correct Answer

D

Explanation

To simplify the expression 2log2/5 - log72/125 + log9, we can use logarithmic properties to combine and simplify the terms.Using the logarithmic property log(a) - log(b) = log(a/b), we can rewrite the expression as:2log(2/5) - log(72/125) + log(9)Next, we can use the logarithmic property log(a) + log(b) = log(ab) to combine the terms:log((2/5)^2) - log(72/125) + log(9)Simplifying further, we have:log(4/25) - log(72/125) + log(9)Using the logarithmic property log(a) - log(b) = log(a/b), we can combine the first two terms:log((4/25)/(72/125)) + log(9)Simplifying the first term inside the logarithm:log((4/25) * (125/72)) + log(9)log(500/180) + log(9)Using the logarithmic property log(a) + log(b) = log(ab), we can combine the terms:log((500/180) * 9)Simplifying the expression inside the logarithm:log(4500/180)log(25)Therefore, the simplified expression is log(25).