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)
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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) (Show Source): You can put this solution on YOUR website!
Since only positive arguments are allowed for the log function.
Answer by rothauserc(4718) (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
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