- #1

gerid21

- 2

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- Homework Statement
- Calculate ##890\times12.34\times0.0637## using logarithms of base 10

- Relevant Equations
- Log tables, calculator

From the log tables:

##log(890) = 2.9494, \space

log(12.34)=1.0913, \space

log(0.0637)=\bar{2}.8041##

I calculate by hand:

##\begin{array}{r}

&2.9494\\

+&1.0913\\&\bar{2}.8041\\\hline &2.8448

\end{array}##

Thus:

##log^{-1}(2.8448) \approx 699.6 \space##

Which is the correct answer.

Now I know ##log(0.0637)=\bar{2}.8041=-2+0.8041=-1.1959##

Yet if I did

##

\begin{array}{r}

&2.9494\\

+&1.0913\\&-1.1959\\\hline &3.2366

\end{array}##

##log^{-1}(3.2366)\approx1724\space## This is obviously wrong.

But if I were to do the problem solely with a calculator, I have to plug in ##log(0.0637)= -1.1959\space## and not ##-2.8041## to get the correct answer. I'm confused at what's going on. I know it has something to do with the negative characteristic of the logarithm. But then if I'm adding it by hand, why doesn't ##-1.1959## work?

##log(890) = 2.9494, \space

log(12.34)=1.0913, \space

log(0.0637)=\bar{2}.8041##

I calculate by hand:

##\begin{array}{r}

&2.9494\\

+&1.0913\\&\bar{2}.8041\\\hline &2.8448

\end{array}##

Thus:

##log^{-1}(2.8448) \approx 699.6 \space##

Which is the correct answer.

Now I know ##log(0.0637)=\bar{2}.8041=-2+0.8041=-1.1959##

Yet if I did

##

\begin{array}{r}

&2.9494\\

+&1.0913\\&-1.1959\\\hline &3.2366

\end{array}##

##log^{-1}(3.2366)\approx1724\space## This is obviously wrong.

But if I were to do the problem solely with a calculator, I have to plug in ##log(0.0637)= -1.1959\space## and not ##-2.8041## to get the correct answer. I'm confused at what's going on. I know it has something to do with the negative characteristic of the logarithm. But then if I'm adding it by hand, why doesn't ##-1.1959## work?

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