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Second Fundamental Theorem of Calculus

Given log10...

Question

Given $l o g_{10} x = a$ and $l o g_{10} y = b$
If $l o g_{10} P = 2 a - b$ ; express P in terms of x and y

A

P = \frac{x}{y}

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B

P = \frac{y}{x}

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C

P = \frac{x^{2}}{y}

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D

P = \frac{y^{2}}{x}

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Solution

The correct option is C $P = \frac{x^{2}}{y}$
Given ${log}_{10} x = a$

and ${log}_{10} y = b$

${log}_{10} P = 2 a - b = 2 {log}_{10} x - {log}_{10} y$
${log}_{10} P = {log}_{10} (\frac{x^{2}}{y})$
$P = \frac{x^{2}}{y}$

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{log}_{10} x = 2 a

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{log}_{10} P = 3 a - 2 b

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