Solving Logarithm with table - A new thread has been created to continue discussion

[chijioke]

I need help with this:




$\displaystyle \text{Evaluate the following by the use of four-figure table.}$





$\displaystyle a.~ 3.025^3 - \sqrt[4]{759.4}$





$\displaystyle b. ~\frac{118.6}{34.95} - \frac{2837}{1964}$





$\displaystyle c. ~\frac{2.874^3+6}{2.874^3-6}$





$\displaystyle d. ~2.908^3 + \sqrt[5]{248.4}$





$\displaystyle e. ~\sqrt[3]{130-\sqrt[3]{130}}$





$\displaystyle f. ~11.65 × 91.21-11.65^2$





$\displaystyle g. ~\sqrt[5]{1.21^4+3.2^3}$





l am having difficulty when it comes to working with problems involving addition and subtractions.




I have no problem working with these ones below because the operations do not involve addition and subtraction. Please take a look at them:




$\displaystyle i. ~\sqrt{\frac{173.8×14.7^2}{2.61^3}}$





$\displaystyle ii. ~\frac{42.79×\sqrt{0.6154}}{8.737×25.61}$





$\displaystyle iii. ~\sqrt[3]{\left(\frac{565×0.0536}{249.1}\right)^2}$




solutions





i.)$\displaystyle i. ~\sqrt{\frac{173.8×14.7^2}{2.61^3}}$





$$\begin{array}{|l|r|} \text{No.} & \text{Log} \\ \hline 173.8 & 2.2400 \\ \hline 14.7^2 & 1.1673 × 2 \\ \hline ~ & = 2.3346 \\ \hline 173.8 × 14.7^2 & 2.2400 \\ ~ & + 2.3346 \\ ~ & \overline{4.5746} \\ \hline 2.61^3 & 0.4166 × 3 \\ \hline ~ & = 1.2499 \\ \hline \frac{173.8 × 14.7^2}{2.61^3} & 4.5746 \\ ~ & -1.2499 \\ ~ & =\\ \hline ~ & 3.3247 \\ \hline \sqrt{\frac{173.8 × 14.7^2}{2.61^3}} & 3.3247 ÷ 2 \\ ~ & = 1.6624 \\ ~ & \text{antilog of} \\ ~ & 1.6624 \bumpeq 45.96 \\ \end{array}$$
$\displaystyle \sqrt{\frac{173.8×14.7^2}{2.61^3}}=45.96$



$\displaystyle ii. ~\frac{42.79×\sqrt{0.6154}}{8.737×25.61}$





$$\begin{array}{|l|r|r|} \text{No.} & \text{Log} & ~ \\ \hline 42.79 & 1.6313 & 1.61313 \\ 0.6154^\frac{1}{2} & \bar{1}.7892 ÷ 2 & ~ \\ ~ & (\bar{1} + 0.7892) ÷ 2 & ~ \\ ~ & (\bar{2} + 0.7892) ÷ 2 & + \\ ~ & (\bar{1} + 0.8946) & \bar{1}.8946 \\ ~ & ~ & \overline{1.5259} \\ 8.737 & 0.9413 & - \\ 25.61 & +1.4084 & 2.3497 \\ \hline 0.1505 & \bar{1}.1762 & ~ \\ \hline \end{array}$$




$\displaystyle ~\frac{42.79×\sqrt{0.6154}}{8.737×25.61} = 0.1501$




$\displaystyle iii. ~\sqrt[3]{\left(\frac{565×0.0536}{249.1}\right)^2}$




$$\begin{array}{|l|r|} \text{Number} & \text{Logarithm} \\ \hline 565 & 2.7520 \\ 0.0536 & \bar{2}.7292 \\ 565 × 0.0536 & \overline{1.4812} \\ 249.1 & 2.3964 \\ \frac{565×0.0536}{249.1} & \overline{\bar{1}.0848} \\ \left(\frac{565×0.0536}{249.1}\right)^2 & \bar{1}.0848 × 2 = \bar{2}.1696 \\ \sqrt[3]{\left(\frac{565×0.0536}{249.1}\right)^2} & = \frac{1}{3}(\bar{2}.1696)=\frac{1}{3}(\bar{3} + 1.1696) \\ ~ & = \bar{1}.389~86 \\ ~ & \bumpeq{\bar{1}.3899} \end{array}$$


$\displaystyle iii. ~\sqrt[3]{\left(\frac{565×0.0536}{249.1}\right)^2}$ $\displaystyle = \text{antilog of}~\bar{1}.3899$



$\displaystyle = 10^{-1} × 2.454$



$\displaystyle = 0.2454$



$\displaystyle = 0.245 (3 \text{s.f})$


I was able to solve i, ii and iii because there was no addition subtraction involved. Now let me take a few shots at some of the problems involving subtraction and addition.


$\displaystyle s1.~ \frac{2.8808^3-1}{2.8808^3+1}$


$\displaystyle s2.~\sqrt[3]{7.9^3 + 2.1^3}$


$\displaystyle s3.~\sqrt{61.73^2 - 38.27^2}$

$\displaystyle s4.~\sqrt[3]{9.58^3 - 7.63^3}$

 

[Steven G]

In 3.025^3 - 4th root(759.4)
Just compute the Log of each number separately.
Give it a try and post back with your work.

 

[Otis]

I need help with this: $\displaystyle \text{Evaluate the following by the use of four-figure table.}$
$\displaystyle a.~ 3.025^3 - \sqrt[4]{759.4}$
$\displaystyle b. ~\frac{118.6}{34.95} - \frac{2837}{1964}$
$\displaystyle c. ~\frac{2.874^3+6}{2.874^3-6}$
$\displaystyle d. ~2.908^3 + \sqrt[5]{248.4}$
$\displaystyle e. ~\sqrt[3]{130-\sqrt[3]{130}}$
$\displaystyle f. ~11.65 × 91.21-11.65^2$
$\displaystyle g. ~\sqrt[5]{1.21^4+3.2^3}$

Hi chijioke. Did you post exercises (a) through (g) above as examples only? I'm not sure where you'd like to begin.

Now let me take a few shots at some of the problems involving subtraction and addition.
$\displaystyle s1.~ \frac{2.8808^3-1}{2.8808^3+1}$
$\displaystyle s2.~\sqrt[3]{7.9^3 + 2.1^3}$
$\displaystyle s3.~\sqrt{61.73^2 - 38.27^2}$
$\displaystyle s4.~\sqrt[3]{9.58^3 - 7.63^3}$

Are these the exercises you'd like help with? Have you seen any lessons, for using the four-figure table approach with expressions that include addition/subtraction? What kind of help would you like?



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[Otis]

I have no problem working with these ones below because the operations do not involve addition and subtraction. Please take a look at them:
$\displaystyle i. ~\sqrt{\frac{173.8×14.7^2}{2.61^3}}$
$\displaystyle ii. ~\frac{42.79×\sqrt{0.6154}}{8.737×25.61}$
$\displaystyle iii. ~\sqrt[3]{\left(\frac{565×0.0536}{249.1}\right)^2}$

You're asking us to check your work on exercises (i) through (iii). Is that correct?



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[chijioke]

Am not through with my typing yet. How I wish this thread can be deleted.

 

[Dr.Peterson]

Am not through with my typing yet. How I wish this thread can be deleted.

Just don't submit it (Post reply) until you have it right. You can see if it is right by using Preview:

​

Also note that you can leave your work and come back later to edit it, and submit when ready.

 

[chijioke]

Thanks I have seen the preview button. Am going to make use of it now instead of posting and deleting continually. But come to think of it, how do I delete or just edit the number 1 thread?

 

[Steven G]

You can only edit a post with about 20 minutes of posting it.

 

[Otis]

how do I delete or just edit the number 1 [post]?

After the time limit expires, you can't. When you're ready to post your revised text, you could start a new thread and ask a moderator to delete this one.

?

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[chijioke]

When you're ready to post your revised text, you could start a new thread and ask a moderator to delete this one.

?

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That's is what I will do. But how do I get the moderator to delete the old thread when am done with the revised one?

 

[Otis]

how do I get the moderator to delete the old thread when am done with the revised one?

ask a moderator to delete this one

The forum allows you to send private messages to other members, including moderators. Click a user name, to open their profile page. Use the 'Start conversation' button.



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[chijioke]

Please whoever is the moderator, help delete this particular thread. I have created a revised thread on this. Thank you.