Counterexample

[Elizabeth1.2]

I would like some help on this problem:

3. Determine if the statement is true or false. If the statement is false, provide an counterexample.

 

[Romsek]

can you determine what [MATH]log_4(1)[/MATH] is equal to?

If you do I think you'll find the answer is obvious.

 

[Dr.Peterson]

I would like some help on this problem:

3. Determine if the statement is true or false. If the statement is false, provide an counterexample.

Saying such a statement is true or false requires defining what d can be. If the claim is that it is true for all real numbers d, then it is false: Choose d=-1 for a simple counterexample! But if d is taken to be positive, just apply some properties of logs. (There are a couple ways to go.)

 

[Steven G]

log₄(3d) is just some unknown number, like x.

If the equation had been x + 7 = x I am sure that you would know if it is valid or not.

Now if the equation had been x + (can't make out because of poor handwriting) = x. Then this equation is true precise when that unclear number is 0.

log₄(1) is your unclear number!

log₄(3d) + log₄(1)=log₄(3d). Now this equation is valid only if log₄(1) = 0.

So as Romsek has pointed out you need to compute log₄(1).

Please post back.

 

[JeffM]

Obviously, Romsek and Jomo are correct. However there is another way to go

[MATH]log_4(3d) + log_4(1) = log_4(3d * 1) = WHAT?[/MATH]
It might be a touch more intuitive.

 

[lookagain]

log₄(3d) + log₄(1)=log₄(3d). Now this equation is valid only if log₄(1) = 0.

and if d > 0.

Ask yourself this, for example:

Is this equation valid, or is there a counterexample?

\(\displaystyle \dfrac{x}{x} \ + \ log(1) \ = \ \dfrac{x}{x} \)