Logarithmic into exponential form

[i-love-physics]

Homework Statement

Write this logarithmic form into exponential form

Homework Equations

N = 0.2 Log4 V

The Attempt at a Solution

I tried

V/0.2 = 4^N

doesnt seem to work.

I've tried doing various inverse functions but that doesn't seem to work either, giving me a headack :(

 

[cepheid]

Hi

I can't understand how you could have obtained the solution you wrote. That having been said, it's the same method for all of these types of questions, right? How can you get rid of the logarithm? By applying the inverse operation, which is taking the exponential. Remember also that what you do to one side of the equation, you must do to the other.

 

[Vagrant]

log p^m can be written as m log p.

 

[i-love-physics]

lets say for example

4 = log3 81

that in exponential form would equal 81 = 3^4

so that means for Y = logb X

The exponential form is X = B^Y

so when i am giving the equation N = 0.2 log4 V

when chaning that to exponential form
does that give me

V = (0.2)(4^N) ?

i just don't get it man...

 

[Vagrant]

no, you either make it N/0.2=logV or N=logV^0.2.
You need to re-read the basics in your textbook.

 

[i-love-physics]

i think i am starting to get it...

In my book it only talks about Y = logb X

It didnt say anything about Y = M logb X

I think i see the picture now.

Thanks for the replys.

 

[i-love-physics]

Is T = n + log2 N
the same as T = Nlog2 N?

How would you write T = n + log2 N
as a exponential form

would it be 2^t-2 = N

or would it be 2^t = N^N

or would it be 2^T/n = N

:(?

 

[cristo]

Is T = n + log2 N
the same as T = Nlog2 N?

no

How would you write T = n + log2 N
as a exponential form

Firstly, you isolate the logarithm; $T-n=log_2 N$
Now, raise each side to the power 2; $2^{T-n}=N$

 

[i-love-physics]

no



Firstly, you isolate the logarithm; $T-n=log_2 N$
Now, raise each side to the power 2; $2^{T-n}=N$

Okay i understand this

but this leads to a more complicated problem

T - N = log2 N

The exponential form therefore equals = 2^x-y = y

NOW, if the question ask you to sketch a graph for this function, how would you do it??, it would be impossible because in order to get the value of "y" you need to know what the exponent x-y is. But you won't know what x-y is because you don't know the value of y.

so let's say for a x value of 1 you would go 2^1-y = y ... then i am stuck...

so what's there to do...? :(


p.s thxs for the replys by the way, i feel this is making progress ( i have clicked on the top adverstisment 10 times already to help support this forum )

 

[Vagrant]

You could write 2^x-y=y as 2^x/2^y=y, or 2^x=y2^y

 

[cepheid]

You could write 2^x-y=y as 2^x/2^y=y, or 2^x=y2^y

In case that's hard to read,

$$2^{x-y} = 2^x2^{-y} = y$$

$$\Rightarrow 2^x = (2^y)y$$