Question

Simplify using properties of logarithms.
log(x) - 1/2log(y)

Answer 1

Is it : \(\log(x) - \cfrac{1}{2} \log (y)\) ?

Answer 2

yes

Answer 3

Fine! So, use the prop. we used in the previous question for the second term - \( a \log x = \log (x^a) \)

Answer 4

So, what is : \(\cfrac{1}{2} \log (y)\) ?

Answer 5

log(y^1/2)

Answer 6

Right, so, we get :

\(\log (x) - \log (y ^{\cfrac{1}{2}})\)

Answer 7

Now, we will use : \(\log a - \log b = \log (\cfrac{a}{b})\)

Answer 8

So, can you simplify the above expression further using the above property.

Answer 9

log(x) / log(y^1/2)

Answer 10

Again , no! You have to put a/b in a single log.

Answer 11

Oh I always hit a bump on that

Answer 12

You need to take care of that. It can harm you in future! Everything else is fine with you :) Just improve this mistake, and you will rock the exams ... :)

Answer 13

log(x / y^1/2)

Answer 14

That's right :) Good work.

You can rationalize it further (the inner fraction)

\(\log (\cfrac{x}{\sqrt{y}}) = \log (\cfrac{x}{\sqrt{y}} \times \cfrac{\sqrt{y}}{\sqrt{y}} ) = \log (\cfrac{x\sqrt{y}}{y})\)

Though, the origial one is good too!

Answer 15

What is the trick to remember all the properties of logarithms? I'm going to put them down on my one page of notes for the exam today

Answer 16

Well, the best trick to remember formulas/properties in Mathematics is to practice a lot. If you practice a lot of questions , then you'll never forget them - that's my personal experience.

For example, you just did a logarithm question like this, and if you do 2-3 more questions like this one, then you will remember the prop. we used here forever. You'll not forget them easily.

Answer 17

We used the product rule and the quotient rule.

Answer 18

Right... !

Answer 19

Also, not to forget power rule.

Answer 20

I got it!