Question-84000

Question Number 84000 by byaw last updated on 08/Mar/20

Commented by Kunal12588 last updated on 08/Mar/20

l o g \sqrt[3]{0.0005957} s h o u l d b e - v e ?

Answered by MJS last updated on 08/Mar/20

\log_{b} 5.957 = . 7750

\Leftrightarrow

5.957 = b^{. 7750}

\sqrt[3]{\frac{5.957}{10000}} = b^{x}

x = \frac{\ln \sqrt[3]{\frac{5.957}{10000}}}{\ln b} = \frac{\frac{1}{3} (\ln 5.957 - 4 \ln 10)}{\ln b} =

= \frac{1}{3} (\frac{\ln 5.957}{\ln b} - \frac{4 \ln 10}{\ln b}) = \frac{1}{3} (\log_{b} 5.957 - {4 \log}_{b} 10) =

= \frac{1}{3} (. 7750 - {4 \log}_{b} 10) =

[b^{. 7750} = 5.957 \Rightarrow b \approx 10]

= - 1.075

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