SOLUTION: What is... Log base 21 (x+4) = 1- log base 21 x And please show me the steps and how you arrived to the answer. Thank you!!

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Question 806443: What is...
Log base 21 (x+4) = 1- log base 21 x
And please show me the steps and how you arrived to the answer. Thank you!!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Log base 21 (x+4) = 1- log base 21 x
we can write it:
log%2821%2C%28x%2B4%29%29 = 1 - log%2821%2C%28x%29%29
Get the logs on the same side of the equation
log%2821%2C%28x%2B4%29%29 + log%2821%2C%28x%29%29 = 1
adding logs, of the same base, is multiply so we have
log%2821%2C%28x%28x%2B4%29%29%29 = 1
The exponent equiv of logs
x(x+4) = 21%5E1
or just
x(x+4) = 21
a quadratic equation
x^2 + 4x - 21 = 0
Factors to
(x+7)(x-3) = 0
our solution has to be positive
x = 3