# 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.

• Many Thanks but the question is how 2.7755 come ? – user360471 Aug 10 '16 at 8:39
• $-1+0.7755=-3+2.7755$ Then we can divide by $3$ – robjohn Aug 10 '16 at 8:39
• 👍 Thanks , Ok now i get it – user360471 Aug 10 '16 at 8:45
• That's the origin for logarithms, doing multiplication and division by means of addition and subtraction while root by means of division. It brings back my memories of looking up mathematical tables instead of using calculators. – Ng Chung Tak Aug 10 '16 at 19:11