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logs equation question HELPP

2log base 3 (x) - log base3 (x-2) = 2
where x > 2

Original post by beth59411

2log base 3 (x) - log base3 (x-2) = 2
where x > 2

Start by using some simple log laws to get the two logarithms together

OP

Original post by AHappyStudent

Start by using some simple log laws to get the two logarithms together

so would it be log base 3 (x^2 /x-2) = 2?

Original post by beth59411

so would it be log base 3 (x^2 /x-2) = 2?

Yep, good work :smile:

:smile:

Now try using the definition of a log to find an equation for x and then solve

By this I mean

Where y = x^n,
n = log base x (y)

OP

Original post by Unknown-99

Here's the worked solution. I wrote it down but couldn't upload the photo so I found a link with the solution.
https://www.symbolab.com/solver/logarithmic-equation-calculator/2%5Clog_%7B3%7D%5Cleft(x%5Cright)-%5Clog_%7B3%7D%5Cleft(x-2%5Cright)%3D2

I managed to work it out thank youuu!!!!

I got the right answer thanks for the help, I always struggle starting it off :/

Here is the solution I wrote it down myself but couldn't upload the photo so here's the worked solution.
https://www.symbolab.com/solver/logarithmic-equation-calculator/2%5Clog_%7B3%7D%5Cleft(x%5Cright)-%5Clog_%7B3%7D%5Cleft(x-2%5Cright)%3D2

Original post by beth59411

I managed to work it out thank youuu!!!!

I got the right answer thanks for the help, I always struggle starting it off :/

No problem. Just remember these 2 simple rules.

- If the logs are ADDED together then combine them by multiplying the things in the brackets by each other.

- If the logs are SUBTRACTED then combine them by dividing the first bracket by the second bracket.

But you can only do this if they have the same base.

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