Finance and logs- question

[4dkids]

My hopes are that some kind soul will take a moment to explain how log is used in this problem:

1.333 = (1+I)n
log 1.3333 = 4 log (1+I)
0.1248 = 4 log (1+I)
.0312 = log (1+I)
1.075 = 1+I

By what means does 'log 1.333' equal 0.1248?

Thank you, in advance, for your help

[barcotta]

Originally Posted by 4dkids

My hopes are that some kind soul will take a moment to explain how log is used in this problem:

1.333 = (1+I)n
log 1.3333 = 4 log (1+I)
0.1248 = 4 log (1+I)
.0312 = log (1+I)
1.075 = 1+I

By what means does 'log 1.333' equal 0.1248?

Thank you, in advance, for your help

I don't personally know the answer--although it all looks vaguely familiar--like a 25 year old memory--but here's a link to a page that explains logarithms and includes examples which look helpful. I'm studying for Principles of Finance next month and if I come across anything that looks like this I'll likely just skip it. I don't recall seeing anything about logs in the specific feedback section...

[4dkids]

Barcotta, Thank you for the reply. I looked at that site and many others with no answer... I believe, at this point, I'm with you and will move on to other topics. If I do find the answer, I will return and post.

[gus]

Originally Posted by 4dkids

By what means does 'log 1.333' equal 0.1248?

That's the easier part of your question:
when there's no base specified in the log notation, it means we're using the default base 10 (which most basic scientific calculators can resolve). You can rewrite Log 1.333 = 0.1248 as 10 raised to the power 0.1248 = 1.333

Try it on your windows calculator in scientific mode, input 1.333 and then press the log button.

And by:

1.333 = (1+I)n
log 1.3333 = 4 log (1+I)

I'm guessing by (1+I)n you meant (1+I) raised to power 4 and that there was some sort of typo or an intermediate step is missing that got us from n to 4.

This following link has some clear explanation:
College Algebra Tutorial on Logarithmic Properties

Please let me know if you need further assistance with logs.

[larry7crys]

If you use your computer's calculator, do the following. Display the Scientific View. This should make the calculator larger and with more functions. Next, enter 1.333 and then press the blue "log" button. This gives the answer of .1248. In the equation, to bring the n down, you would have to take the "log" of both sides. I don't know were the 4 comes from but hopefully that helped some. Good Luck!

[4dkids]

The light is going on!! This is the whole example:

$100,000 = 75,000 x (1+I)4
$100,000/75,000 = (1+I)4
1.3333 = (1+I)4
log 1.3333 = 4 log (1+I)
0.1248 = 4 log (1+I)
0.0312 = log (1+I)
1.075 = 1+I
0.075 = I

What, then, is the value of log to give the answer in red?

Barcotta, Larry7crys and Gus... thank you!! I said I would move on to other topics, but I've not stopped looking for the solution.

[gus]

Actually 0.0312 would be the value of the log function to be exact, i.e., if you raise 10 to the power 0.0312 you would get 1+I as a result:

log (1+I) = 0.0312 can be re-written as 10^0.0312 = 1+I (the caret symbol ^ here meaning raised to the power, I could not find out how to write in superscript))

Since we're interested in finding out the value of I, we now solve for 1+I by simply performing the calculation 10^0.0312 on the calculator in scientific mode:

Input 10
Press x^y purple button in the center left side
Input 0.0312

You'll get a number 1.074481.... which can be rounded to 1.075, thus 1+I = 1.075. Subtracting 1 from each side of the equation gives the value of I = 0.075 (I'm sure this step was self explanatory).

[larry7crys]

I agree with Gus. Since you would have to eliminate the log from the right hand side, you would take the left hand side and place it in this format 10^n, where n is 0.0312, which equals to 1.075.