SOLUTION: slove for x: log (x+2) - log (x-1)= log 4 3 3 3 please show work

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Question 244407: slove for x:
log (x+2) - log (x-1)= log 4
3 3 3
please show work
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C%28x%2B2%29%29-log%283%2C%28x-1%29%29=log%283%2C4%29
log%283%2C%28x%2B2%29%2F%28x-1%29%29=log%283%2C4%29

Therefore, %28x%2B2%29%2F%28x-1%29=4
%28x%2B2%29=4%28x-1%29
x%2B2=4x-4
6=3x
x=2

Check: There are NO cases in which x=2 results in a log of a negative, so the answer checks! Actually, it really can be checked, by substituting x=2:
log%283%2C4%29-log%283%2C1%29+=+log%283%2C4%29
log%283%2C4%29+-+0+=+log%283%2C4%29

If you need additional help with the topic of LOGARITHMS, please see my website. Click on my tutor name "Rapaljer" anywhere in algebra.com, which will take you to my Homepage. On my Homepage, look for "Basic, Intermediate, and College Alegebra: One Step at a Time". Choose "College Algebra", look in "Chapter 4" for my complete nontraditional, explanation of Logarithms. This particular question actually comes from "Section 4.04 Exponential and Logarithmic Equations." These lessons are supported by my MATH IN LIVING COLOR pages.

In addition, there are TWO two hour videos of me teaching the topic of Logarithms in my own classroom a few years aog. These are FREE. To see the videos, look on my Homepage for "Rapalje Vidoes in Living Color." Choose "College Algebra" and look for "Logarithms Part II."

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida