# SOLUTION: find x, Log{base x}5=8+Log{base 9}x for the left x is the base. for right 9 is the base.

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Question 449498: find x,
Log{base x}5=8+Log{base 9}x
for the left x is the base. for right 9 is the base.

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log(5)/log(x) = 8 + log(x)/log(9) = [8*log(9) + log(x)]/log(9)
log(5)/log(x) = (8*log(9) + log(x))/log(9)
log(5)*log(9) = log(x)*(8log(9) + log(x))

Sub u for log(x)

 Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=5825.03604476 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.00873812546124952, -76.3306618745387. Here's your graph:

x1 and x2 are the logs of x.
x = 0.980080785
x = 4.670228502E-77