Using Logarithm Tables to find values in an old trig book

[cbarker1]

Hi Everyone, I need some help using five-place table to find the value of this logarithm. $\log_{10}\left({0.002261}\right)$=

$\log_{10}\left({2.261*10^{-3}}\right)$

I use the multiplication to sum rule for logarithms hence

$(\log_{10}\left({2.261}\right)-3+10)-10$

N	0	1	2
220	34 242	262	282
221	34 439	459	479
222	34 635	655	674
223	34 830	850	869
224	35 025	044	064
225	35 218	238	257
226	35 411	430	449

I look up the value of the log.

$\log_{10}\left({2.261}\right)$+(-3+10)-10=.35430+7-10

However the book said to +10 to the logarithm then subtract 10 from the value; thus, the answer is: 7.35430-10. When I checked on the calculator for the value of the log is -2.64569, i got the wrong answer. Thank for your help.

 

[jvicens]

Hi there,

Thank you for reaching out for help with using the five-place table to find the value of a logarithm. I can see that you have correctly used the multiplication to sum rule for logarithms, but there seems to be a small misunderstanding in the final steps.

Let's take a closer look at the table you have provided. The first column represents the power of 10, and the second column represents the value of the logarithm for that power of 10. For example, at power of 10 = 0, the value of the logarithm is 0. At power of 10 = 1, the value of the logarithm is 1. At power of 10 = 2, the value of the logarithm is 2, and so on.

Now, let's take a look at the value you are trying to find the logarithm for, which is 0.002261. This number can also be written as 2.261 * 10^-3. Looking at the table, we can see that the power of 10 for this number is -3, and the value of the logarithm for this power of 10 is 0.35430. This means that the value of the logarithm for 2.261 * 10^-3 is 0.35430.

However, the book has asked you to add 10 to the logarithm and then subtract 10 from the value. This is because the table only provides values for the logarithm between 0 and 1. So, to find the value of the logarithm for a number less than 1, we add 10 to the logarithm and then subtract 10 from the value.

In this case, the value of the logarithm for 2.261 * 10^-3 is 0.35430. Adding 10 to this value gives us 10.35430, and subtracting 10 from the value gives us 0.35430. This is the final answer, which is 0.35430.

I hope this helps clarify the process for finding the value of a logarithm using the five-place table. Please let me know if you have any further questions or need any additional assistance.