Simple log question - need help! (1 Viewer)

[Coookies]

This is from cambridge, how do I fill in the values?
This sounds really stupid but isn't the log button on the calculator for base 10? So do I have to convert this manually?

 

[nightweaver066]

May sound annoying but you can use change of base law.

where x, y and a are > 0.

 

[Coookies]

Is that the only thing you can use?
Can you use the y=logay?

 

[AAEldar]

And so on.

 

[Parvee]

I think it would be easier if you use:
loga(x/y)=logax-logay
and then you use change of base.

 

[AAEldar]

I think it would be easier if you use:
loga(x/y)=logax-logay
and then you use change of base.

There is no need for any change of base here. All those numbers given are powers of 2, and the base is 2 so you can simplify with ease.

 

[qwerty44]

Well you don't really need a calculator, because they are simple numbers.


For example:


And:...and so on....



However if you do want to use calculator put in:





EDIT: Im way too slow with latex....

 

[Parvee]

There is no need for any change of base here. All those numbers given are powers of 2, and the base is 2 so you can simplify with ease.

Oh I didn't notice that.
The method was just a general one for any type of these questions

 

[Coookies]

AAEldar's way was best, nice and simple
But you've all helped, repped all

Thanks!!

 

[Drongoski]

You started out right. But last few steps redundant.

immediately by definition. Change of base is unnecessary.

Similarly by definition of log:

 

[Coookies]

^ I didn't know you could do that lol!
What definition is it?

 

[zeebobDD]

if you get one of those beast calculators, you can use any base but i don't think their allowed by BoS

 

[Drongoski]

^ I didn't know you could do that lol!
What definition is it?

What?

The log of a number to a base 'b' is what its power (i.e. exponent) is to that base 'b'. e.g.

since 343 = 7³

Not knowing this explains your difficulty with something as trivial as your question.

 

[Coookies]

What?

You said "immediately by definition"
Whats the definition? eg. y=a^x something like that

 

[Coookies]

New question:

Solve to 4 sig figs.
5^x = 150
(not sure how to type in into the calculator)

 

[Coookies]

What?

The log of a number to a base 'b' is what its power (i.e. exponent) is to that base 'b'. e.g.

since 343 = 7³

Not knowing this explains your difficulty with something as trivial as your question.

Ahhh, I see it now, thanks!

 

[Timske]

Log150/Log5 = 3.113

:. x = 3.113

 

[Drongoski]

You said "immediately by definition"
Whats the definition? eg. y=a^x something like that

Then, straight away:



If you had to resort to use of "change of base" in your original question, your understanding of logs is poor.

If you use a calculator, I don't know what to say!

In Timske's solution above, the use of "change of base" is justified.

 

[Coookies]

Then, straight away:



If you had to resort to use of "change of base" in your original question, your understanding of logs is poor.

If you use a calculator, I don't know what to say!

In Timske's solution above, the use of "change of base" is justified.

Lol, I wasn't going to change the base. I was thinking of the law that I typed
Also, the calculator didn't cross my mind

 

[Drongoski]

Lol, I wasn't going to change the base. I was thinking of the law that I typed
Also, the calculator didn't cross my mind

I did not have you in mind!