SOLUTION: Hello, I am having a problem with figuring this problem. I have been trying to figure out how you come up with the answers and how to solve it. Ln(12000 divided by 25000) Thi

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Hello, I am having a problem with figuring this problem. I have been trying to figure out how you come up with the answers and how to solve it. Ln(12000 divided by 25000) Thi      Log On


   

Question 84553: Hello,
I am having a problem with figuring this problem. I have been trying to figure out how you come up with the answers and how to solve it.
Ln(12000 divided by 25000)
This is underlined and underneath is
0.075
Thanks for your help
Michelle
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
If I understand your problem correctly, it is:
.
%28ln%2812000%2F25000%29%29%2F0.075
.
If this is your problem, the first thing you can do is to cancel the zeros in the numerator
with those of the denominator to get:
.
%28ln%2812%2F25%29%29%2F0.075
.
You can now recognize that you are taking the natural logarithm of a division. By the rules
of logarithms you can write this as the difference of two logarithms ... the logarithm
of the numerator minus the logarithm of the denominator. So your problem is equivalent to:
.
%28ln%2812%29-ln%2825%29%29%2F0.075
.
You can now use a scientific calculator to find that ln%2812%29+=+2.48490665 and that
ln%2825%29+=+3.218875825
.
Substituting these two values into the problem makes it become:
.
%282.48490665+-+3.218875825%29%2F0.075
.
Performing the subtraction in the numerator results in the problem becoming:
.
-0.733969175%2F0.075
.
and, finally, doing the division results in an answer of:
.
-9.786255668
.
And since we used a scientific calculator to find ln(12) and ln(25) we could have done
the whole thing on a scientific calculator from the very start. Basically, it could have
been done on a typical calculator as follows:
.
Enter 12000
Press the divide key
Enter 25000
Press the "=" key
At this point you have found 12000 divided by 25000
Press the natural logarithm "ln" key
The above step gives you the natural logarithm of 12000 divided by 25000
Press the divide key
Enter 0.075
Press the "=" key
.
You should have the answer of -9.786255668 which agrees with what we got by going
through a few more steps. But I suppose it was OK to do the extra steps just for practice.
.
Hope this helps you to understand logarithms in general a little better, and how to work
with natural logarithms in particular.
.
If I mis-interpreted what you meant your original problem to be, please repost the entire
problem.