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mcapone888

Novice

Registered: 2023-03-07

Posts: 2

Pre-Calculus - Need help condensing logarithm that starts with a -

Hi everyone.

I feel I have a good handle on expanding and condensing logarithms, but I saw a problem on a test prep sheet that threw me:

- ln(5) - ln(3) - 16 ln(x)

Almost all of my problems like this up to this point started with a positive. So I would take the positives and put them in the numerator and put anything that started with a negative in the denominator. But these are all negatives. Should I multiply all values by -1 turning them all positive and then condensing them using multiplication instead? Or maybe I should put a 1 in the numerator and everything else in the denominator?

Note - I know to move the 16 to the exponent spot of the x, but I have no idea what I should do about that negative sign that starts everything off?

Please help? If possible, I am looking for a quick explanation and not just the answer (in case I come across more like these).  Thanks!!!

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Pre-Calculus - Need help condensing logarithm that starts with a -

hi mcapone888

Welcome to the forum.

There are three rules that will cover most of these questions.

These work whatever the log base so work for ln(x) too.

Let's deal with the easier bit first.

The negatives mean all three must end up on the bottom of a fraction, so what goes on top?

Think of it as 0 -  ln(5) - ln(3) - 16 ln(x)

So now write 0 as a log.

so the top number for the fraction is 1.

Can you finish this from here?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mcapone888

Novice

Registered: 2023-03-07

Posts: 2

Re: Pre-Calculus - Need help condensing logarithm that starts with a -

I am thinking:

1 / 15x^16

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Pre-Calculus - Need help condensing logarithm that starts with a -

hi mcapone888

Yes, that's it!  But don't forget the ln

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob