# Log4 x - log4 (x-3) = 5

1. Jul 6, 2011

### nae99

1. The problem statement, all variables and given/known data

log4 x - log4 (x-3) = 5

2. Relevant equations

3. The attempt at a solution

log4 x/x-3 = 5

Last edited by a moderator: May 12, 2014
2. Jul 6, 2011

### dextercioby

Re: logarithm

OK, so it's something like

$$\log_{4} \frac{x}{x-3} = 5$$

What do you do next ?

3. Jul 6, 2011

### nae99

Re: logarithm

i think

x/ x-3 = 4^5

4. Jul 6, 2011

### dextercioby

Re: logarithm

Good thinking. Next ?

5. Jul 6, 2011

### nae99

Re: logarithm

x$/$ x-3 = 1024

6. Jul 6, 2011

### dextercioby

Re: logarithm

So it's very easy to find the x, right ?

7. Jul 6, 2011

### nae99

Re: logarithm

no thats where i am stuck

8. Jul 6, 2011

### nae99

Re: logarithm

i would probably do this:

x = 1024 (x-3)

9. Jul 6, 2011

### nae99

Re: logarithm

??

10. Jul 6, 2011

### dextercioby

Re: logarithm

So it's like 3072 = 1023 x. Do you agree ?

11. Jul 6, 2011

### nae99

Re: logarithm

yes now it will be
x = 1023x - 3072

12. Jul 6, 2011

### dextercioby

Re: logarithm

I think you're missing something very simple. You've got an equation in which you must what numerical value hides under 'x'.

So $x= 1024\cdot (x-3) = 1024\cdot x - 1024\cdot 3 = 1024\cdot x - 3072$

Now subtract x from both terms of $x= 1024\cdot x - 3072$.

What do you get ?

13. Jul 7, 2011

### nae99

Re: logarithm

ok, so if i am going to subtract x from both terms, i would end up with:

x = 1024 - 3072

14. Jul 7, 2011

### nae99

Re: logarithm

x = 1024 - 3072

15. Jul 7, 2011

### Mentallic

Re: logarithm

What?

Don't you know basic algebra? Solve for x in 3x=x+2, now apply the same idea to solve for x in x=1024x-3072

16. Jul 7, 2011

### nae99

Re: logarithm

as u can see i am not good at this, ok here goes

1024x-x=3072
1023x = 3072

17. Jul 7, 2011

### Mentallic

Re: logarithm

Well then you need to go back and cover basic algebra again. You can't afford to lose that many marks on logarithms just because you don't know your algebra.

Yes and now? If I asked you to solve for x why haven't you given us x=... ?

18. Jul 7, 2011

### nae99

Re: logarithm

x = 3072-1023
x = 2049

19. Jul 7, 2011

### Mentallic

Re: logarithm

No, it's not 1023+x=3072, it's 1023x=3072. You really need to go back and catch up on what you've missed out on.

20. Jul 7, 2011

### nae99

Re: logarithm

so i would divide both sides by 1023

1023x = 3072

1023x/1023 = 3072/1023