Which of these statements about y = 8{m} is correct?

Correct Answer is : log y = 3 log 2 + 12\; 1/221 log m

Correct Answer is : log y = 3 log 2 + 12\; 1/221 log m

Test Index

WAEC Mathematics 2012 Paper

Question : 21

Total: 49

\sqrt{m}

is correct?

Solution:

Concept:

Simplify the logarithm of the given expression using the product law and power law of logarithms.

Explanation:

Given that

y = 8\sqrt{m}

, take logarithms on both sides.

\log y = \log\left(8\sqrt{m}\right)

Apply the product law

\log(AB) = \log A + \log B

\log y = \log 8 + \log\sqrt{m}

Since

8 = 2^3

and

\sqrt{m} = m^{\frac{1}{2}}

, rewrite the terms accordingly.

\log y = \log\left(2^3\right) + \log\left(m^{\frac{1}{2}}\right)

Now apply the power law

\log(a^n) = n\log a

\log y = 3\log 2 + \frac{1}{2}\log m

This result matches the expression given in option D.

Answer:

Option D:

\log y = 3\log 2 + \frac{1}{2}\log m

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