Evaluate log5(y² x^5 ÷ 125 b¹/2})

Correct Answer is : 2log5y + 5log5x − ½ log5b −3

2log 5 y + 5log 5 x − ½ log 5 b −3

Correct Answer is : 2log5y + 5log5x − ½ log5b −3

Test Index

JAMB Mathematics 2015 Paper

Question : 42

Total: 61

Evaluate log5(

y^2 x^5 \div 125 b^{\frac{1}{2}})

Solution:

Concept:

Use the laws of logarithms for division, multiplication, and powers, then simplify

\log_{5}125

Explanation:

Start with

\log_{5}\left(y^{2} x^{5} \div 125 b^{\frac{1}{2}}\right)

Rewrite as a fraction:

\log_{5}\left(\frac{y^{2}x^{5}}{125b^{1/2}}\right)

Apply the quotient rule:

\log_{5}(y^{2}x^{5}) - \log_{5}(125b^{1/2})

Use the product rule on each group:

\log_{5}y^{2} + \log_{5}x^{5} - \left(\log_{5}125 + \log_{5}b^{1/2}\right)

Apply the power rule:

2\log_{5}y + 5\log_{5}x - \log_{5}125 - \frac{1}{2}\log_{5}b

Since

125 = 5^{3}

, we have

\log_{5}125 = 3

Therefore, the expression simplifies to

2\log_{5}y + 5\log_{5}x - \frac{1}{2}\log_{5}b - 3

Answer:

2\log_{5}y + 5\log_{5}x - \frac{1}{2}\log_{5}b - 3

This matches option D.

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