Find the range of values that x can take if 9 log_x 5=log_5 x I'm stuck on a homework question about logarithms. I can't work out how to do it, and all I've managed to do is turn 9 log_x 5 into log_x 5^9. Can anyone guide me onto the right path to solve this?

Paige Vasquez

Paige Vasquez

Open question

2022-08-30

Find the range of values that x can take if 9 log x 5 = log 5 x
I'm stuck on a homework question about logarithms. I can't work out how to do it, and all I've managed to do is turn 9 log x 5 into log x 5 9 . Can anyone guide me onto the right path to solve this?

Answer & Explanation

arbustekp

arbustekp

Beginner2022-08-31Added 8 answers

If you prefer to use powers rather than logs you can proceed in this way:
Let L = log 5 x so that x = 5 L and 5 = x 1 L so that log x 5 = 1 L
We then have 9 1 L = L so that 9 = L 2 and L = ± 3 so that x = 5 3 or x = 5 3

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