SOLUTION: Determine the real solutions to the system of nonlinear equations. y=log_4(x+6)+9 y=11-log_4(x+21) Write solution(s) in ordered pair

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Determine the real solutions to the system of nonlinear equations. y=log_4(x+6)+9 y=11-log_4(x+21) Write solution(s) in ordered pair      Log On


   

Question 1094820: Determine the real solutions to the system of nonlinear equations.
y=log_4(x+6)+9
y=11-log_4(x+21)
Write solution(s) in ordered pair
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!

No solution.

log_4%28x%2B6%29%2B9+=+11-log_4%28x%2B21%29
log_4%28x%2B6%29%2Blog_4%28x%2B21%29+=+11-9+=+2
log_4%28x%2B6%29%2Blog_4%28x%2B21%29+=+log_4%2816%29
%28x%2B6%29%28x%2B21%29+=+16
x%5E2%2B27x%2B126+=+16
x%5E2%2B27x%2B110+=+0
%28x%2B5%29%28x%2B22%29+=+0

The two solutions to the quadratic equation are x = -5 and x = -22.

But both of those solutions, tried in the original equations, result in trying to evaluate the log of a negative number.