# How to find $\sqrt[3]{0.5964}$ using logarithms? [closed]

\begin{align*} \sqrt[3]{0.5964} &= \left(0.5964\right)^{\frac{1}{3}}\\ \log \sqrt[3]{0.5964} &= \frac{1}{3} \log 0.5964\\ &= \frac{1}{3} \cdot\overline{1}.7755\\ &= \frac{1}{3}\cdot\left(\overline{3} +2.7755\right)\\ &= \overline{1}.9252 \end{align*}

Can anyone explain what happened in line 4

Many Thanks

## closed as unclear what you're asking by Did, 5xum, PSPACEhard, user99914, BruceETAug 10 '16 at 19:57

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• Nobody can explain this, because nobody can read it. – 5xum Aug 10 '16 at 8:25
• Does ${\overline{1}}$ and ${\overline{3}}$ mean to subtract that digit? – robjohn Aug 10 '16 at 8:33
• no it means bar 1 and 3 or negative 1 & 3 – user360471 Aug 10 '16 at 8:34
• So it means to subtract that digit. – robjohn Aug 10 '16 at 8:34
• Please take a look at our tutorial so that you can type your posts properly here. – Em. Aug 10 '16 at 8:35

My guess is that $$\overline{1}.7755=-1+0.7755=-3+2.7755$$ Then divide by $3$ to get $$-1+0.9252=\overline{1}.9252$$ This is a way of keeping a positive mantissa.
• $-1+0.7755=-3+2.7755$ Then we can divide by $3$ – robjohn Aug 10 '16 at 8:39