Question 1090405: solve for x. log X base5= log5 base X +2
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The equation is
log_5(x) = log_x(5)+2
Use the fact that log_a(b) and log_b(a) are reciprocals to rewrite log_x(5) as 1/log_5(x):
log_5(x) = 1/log_5(x) + 2
Then multiply both sides by log_5(x) to yield a quadratic equation with log_5(x) as the "variable":
(log_5(x))^2 = 1 + 2log_5(x)
(log_5(x))^2 - 2log_5(x) - 1 = 0
Then use the quadratic formula to find the two values of log_5(x), and from those value find the two values of x.
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