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MATHEMATICS

JAMB 2007 - Question 33

Mathematics 2007 JAMB Past Questions - Question 33: If log102 = x, express log10 12.5 in terms of x

If log102 = x, express log10 12.5 in terms of x

A: 2(1+x)

B: 2+3x

C: 2(1-x)

D: 2-3x

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Correct Answer

Explanation

logâ‚�â‚€¹²âˆ™â�µ = logâ‚�â‚€²â�µâˆ•â‚‚ = logâ‚�â‚€²â�µ - logâ‚�â‚€² = logâ‚�â‚€5² - logâ‚�â‚€²→ 2 logâ‚�â‚€â�µ - logâ‚�â‚€² = 2 → (Lâ‚�â‚€ 10/2) - logâ‚€²→ 2 (logâ‚�â‚€ 10 - logâ‚�â‚€2) - logâ‚�â‚€→ 2(1 –x ) – x → 2 – 2x – x = 2- 3xTo express logâ‚�â‚€ 12.5 in terms of x, we can use the properties of logarithms.We know that logâ‚�â‚€ 2 = x. This means that 10 raised to the power of x equals 2:10^x = 2Now, let's express 12.5 as a power of 10:12.5 = 10^yTo find y, we can take the logarithm of both sides with base 10:logâ‚�â‚€ 12.5 = logâ‚�â‚€ (10^y)Using the property of logarithms, logâ‚� (a^b) = b, we can simplify the equation:logâ‚�â‚€ 12.5 = yTherefore, logâ‚�â‚€ 12.5 can be expressed in terms of x as y.