SOLUTION: Hello, I need help solving this equation. I am supposed to show all steps to solve for x. log_(3)x+log_(3)(x+5)=9

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Question 1206117: Hello, I need help solving this equation. I am supposed to show all steps to solve for x.
log_(3)x+log_(3)(x+5)=9

Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
log(3,x)+log(3,(x+5))=9


if switch to exponential form

You take it from here?

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!



use log rule that log(A)+log(B) = log(A*B)

convert from log form to exponent form







Apply the quadratic formula where a = 1, b = 5, c = -19683








or

or both of which are approximate

Since the domain of log(x) is x > 0, it rules out as a possible solution.

Therefore, we go with as the only possible solution.

I used WolframAlpha to confirm the answer is correct.
https://www.wolframalpha.com/input?i=log_%283%29x%2Blog_%283%29%28x%2B5%29%3D9

Another way to confirm the answer is to let
f(x) = log(x)/log(3) + log(x+5)/log(3)
Note the use of the change of base formula.
Then you should find that f(137.818388) = 9 approximately.

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