How do you expand this logarithm? ${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

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How do you expand this logarithm? ${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

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Answer 1 · 2017-02-12T16:47:37

${log}_{4} \sqrt[3]{x} = \frac{1}{3} {log}_{4} x = \frac{1}{3} \frac{log x}{log 4} = 0.5537 log x$ $log_4root(3)x=1/3log_4x=1/3logx/log4=0.5537logx$

Explanation:

As #log_aroot(n)x=log_a(x)^(1/n)=1/nlog_ax,

As such ${log}_{4} \sqrt[3]{x} = {log}_{4} {(x)}^{\frac{1}{3}} = \frac{1}{3} {log}_{4} x$ $log_4root(3)x=log_4(x)^(1/3)=1/3log_4x$

but as ${log}_{a} b = \frac{log b}{log a}$ $log_ab=logb/loga$

${log}_{4} \sqrt[3]{x} = \frac{1}{3} \frac{log x}{log 4} = \frac{1}{3} \frac{log x}{0.6021} = 0.5537 x$ $log_4root(3)x=1/3logx/log4=1/3logx/0.6021=0.5537x$

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How do you expand this logarithm? ${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

1 Answer

Explanation:

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How do you expand this logarithm? ${log}_{4} \sqrt{x^{3}}$ $log_(4)sqrt(x^3)$

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