SOLUTION: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) log(x + 4) = 1 − log(x − 3)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) log(x + 4) = 1 − log(x − 3)      Log On


   

Question 965209: Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
log(x + 4) = 1 − log(x − 3)
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%28x%2B4%29%29%2Blog%28%28x-3%29%29=1
log%28%28x%2B4%29%28x-3%29%29=1
x%5E2%2Bx-12=10
x%5E2%2Bx-22=0
x%5E2%2Bx%2B1%2F4-22=1%2F4
%28x%2B1%2F2%29%5E2=88%2F4%2B1%2F4
%28x%2B1%2F2%29%5E2=89%2F4
x%2B1%2F2=0+%2B-+sqrt%2889%29%2F2
x=-1%2F2+%2B-+sqrt%2889%2F2%29
Since only positive arguments are allowed for the log function.
highlight%28x=%28sqrt%2889%29-1%29%2F2%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
log(x + 4) = 1 − log(x − 3)
add log(x - 3) to both sides of =
log(x + 4) + log(x - 3) = 1
log (x^2 +x -12) = 1
apply definition of log
x^2 +x -12 = 10
x^2 +x -22 = 0
using quadratic formula
x = (-1 + sqrt(1 - 4*1*(-22))) / (2*1) = 4.216990566
x = (-1 - sqrt(1 - 4*1*(-22))) / (2*1) = −5.216990566
we only want the positive value for x since logarithm is not defined for negative numbers
*****************************************************
x = 4.216990566
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check the answer
log(4.216990566 + 4) = 1 − log(4.216990566 − 3)
log( 8.216990566 ) = 1 - log( 1.216990566 )
0.914712788 = 1 - 0.085287212 = 0.914712788
our answer checks