Numbers of solutions of the equation log_3(2x^2+3x+3)/(5) = 1/(log_(2x^2+3x+9)9)

klasyvea

klasyvea

Answered question

2022-11-20

Numbers of solutions of the equation log 3 2 x 2 + 3 x + 3 5 = 1 log 2 x 2 + 3 x + 9 9
Pretty straightforward question. When I solved it, I got two positive and two negative solutions, so that would make 4 in total. None get discarded as the arguments in the logarithm still stay positive.
However, the solution is supposed to be 2, so I'm not sure where I went wrong.
I got the values of x as 2, 1 / 2, 12 / 5 and 18 / 5

Answer & Explanation

Gilbert Petty

Gilbert Petty

Beginner2022-11-21Added 23 answers

You need to use the change of base formula:
l o g a x = log b x log b a
Remove the polynomial from the base of the log on the right by changing the base to 3

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