SOLUTION: solve the equation ln(x+5)-ln(3)=ln(x-3) a. 2.5 b. 4.5 c. 5 d. 7

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve the equation ln(x+5)-ln(3)=ln(x-3) a. 2.5 b. 4.5 c. 5 d. 7      Log On


   

Question 79502: solve the equation ln(x+5)-ln(3)=ln(x-3)
a. 2.5
b. 4.5
c. 5
d. 7
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
ln%28x%2B5%29-ln%283%29=ln%28x-3%29
Use the rule log%28a%2Fb%29+=+log%28a%29+-+log%28b%29 (use it backwards)
ln%28%28x%2B5%29%2F3%29+=+ln%28x-3%29
If the natural logs are equal, then the quantities themselves have to
be equal
%28x%2B5%29%2F3+=+x-3
x%2B5+=+3%2A%28x-3%29
x%2B5+=+3x+-9
2x+=+14
x+=+7 answer
now check answer
ln%28x%2B5%29-ln%283%29=ln%28x-3%29
ln%287%2B5%29-ln%283%29=ln%287-3%29
ln%2812%29+-+ln%283%29+=+ln%284%29
ln%2812%2F3%29+=+ln%284%29
ln%284%29+=+ln%284%29
OK