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Definition of Functions

Given that ...

Question

Given that ${log}_{10} y + 2 {log}_{10} x = 2$ , express y in terms of x .

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Solution

Given:
${log}_{10} y + 2 {log}_{10} x = 2$
Let us simplify the given expression,
${log}_{10} y + {log}_{10} x^{2} = 2 {log}_{10} 10$
${log}_{10} (y \times x^{2}) = {log}_{10} 10^{2}$
$y x^{2} = 100$
$y = 100 / x^{2}$

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Q. Express y in terms of x, given that

\frac{x}{5} + 2 y = 3

. Check whether (−5, 2) is a solution of the given equation.

l o g_{10} x = a

l o g_{10} y = b

l o g_{10} P = 2 a - b

; express P in terms of x and y

a^{2} = l o g_{10} x, b^{3} = l o g_{10} y

\frac{a^{2}}{2} - \frac{b^{3}}{3} = l o g_{10^{z}}

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{log}_{10} x = 2 a

{log}_{10} y = \frac{b}{2}

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

, then P in terms of

x

y

{log}_{10} x = a

{log}_{10} y = b

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