How do you condense ${log}_{10} x - 4 {log}_{10} y$ $log_10 x - 4log_10 y$ ?

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How do you condense ${log}_{10} x - 4 {log}_{10} y$ $log_10 x - 4log_10 y$ ?

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Answer 1 · 2018-04-16T13:27:35

${log}_{10} (\frac{x}{y^{4}})$ $log_(10)(x/y^4)$

Explanation:

$using the laws of logarithms$ $"using the "color(blue)"laws of logarithms"$

$∙ x {log x}^{n} \Leftrightarrow n log x$ $•color(white)(x)logx^nhArrnlogx$

$\Rightarrow 4 {log}_{10} y = {log}_{10} y^{4}$ $rArr4log_(10)y=log_(10)y^4$

$∙ x log x - log y \Leftrightarrow log (\frac{x}{y})$ $•color(white)(x)logx-logyhArrlog(x/y)$

$\Rightarrow {log}_{10} x - {log}_{10} y^{4} = {log}_{10} (\frac{x}{y^{4}})$ $rArrlog_(10)x-log_(10)y^4=log_(10)(x/y^4)$

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How do you condense ${log}_{10} x - 4 {log}_{10} y$ $log_10 x - 4log_10 y$ ?

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How do you condense ${log}_{10} x - 4 {log}_{10} y$ $log_10 x - 4log_10 y$ ?