Question 1090405
<br>The equation is<br>
log_5(x) = log_x(5)+2<br>
Use the fact that log_a(b) and log_b(a) are reciprocals to rewrite log_x(5) as 1/log_5(x):<br>
log_5(x) = 1/log_5(x) + 2<br>
Then multiply both sides by log_5(x) to yield a quadratic equation with log_5(x) as the "variable":<br>
(log_5(x))^2 = 1 + 2log_5(x)<br>
(log_5(x))^2 - 2log_5(x) - 1 = 0<br>
Then use the quadratic formula to find the two values of log_5(x), and from those value find the two values of x.