# (log√125 + log √27 - √8)/ log 15 - log 2 = 3/2

1. Nov 16, 2012

### lionely

1)Without using tables, show that

(log√125 + log √27 - √8)/ log 15 - log 2 = 3/2

What i tried was

(3/2 log 5 + 3/2 log 3 - 3/2 log 2)/ log 5+log 3 - log2

then from here I don't know where to take it.

2) Find the value of x if log x2/ log a^2 = log y^4/logy

I tried this 2logx - 2loga = 4 log y- log y
2logx = 3logy+ 2 loga

then here I get stuck..

Last edited by a moderator: Feb 6, 2013
2. Nov 16, 2012

### ehild

Re: Logs

You miss some parentheses.

ehild

3. Nov 16, 2012

### Mentallic

Re: Logs

Since you want the problem to reduce to something simple (3/2) you should combine the log terms and simplify from there.

If we have

$$\log(x)=y$$ then what is x?

4. Nov 16, 2012

### lionely

Re: Logs

10^y = x?

5. Nov 16, 2012

### Mentallic

Re: Logs

Yes, so now do the same thing. Set the equation so that it is in the form $\log(x)=y$ and then make x the subject. Oh and y will be some complicated expression.

And once you've done that, remember the rules

$$a^{x+y}=a^xa^y$$

$$a^{\log_{a}(x)}=x$$

6. Nov 16, 2012

### lionely

Re: Logs

I'm kind of confused if I have this

log x = 3logy - 2loga

I duno how to get rid of log a to make it log (x) = y

7. Nov 16, 2012

### ehild

Re: Logs

log y^4/logy=4log(y)/log(y)=4

ehild

8. Nov 16, 2012

### lionely

Re: Logs

oh.. so it's 2log x = 4 + 2log a

x^2= a^8

x=a^4?

9. Nov 16, 2012

### Mentallic

Re: Logs

ehild noticed some mistakes which you should first address.

$$\frac{\log(a)}{\log(b)}\neq \log(a)-\log(b)$$

What you're thinking of is

$$\log\left(\frac{a}{b}\right)=\log(a)-\log(b)$$

10. Nov 16, 2012

### lionely

Re: Logs

Oh, Umm should it should be

log x^2/ log a^2 = 4

2log x = 8 log a

log x = 4log a

10^a^4 = 10^x

x= a^4?

11. Nov 16, 2012

### lionely

Re: Logs

And for the first one

is it (3/2log5 + 3/2log 3 - 3/2log 2)/ (log 5+ log 3) - log 2

= 1/2log log + 1/2log 3 - 1/2log2?

12. Nov 16, 2012

### ehild

Re: Logs

I think you made some mistake when copying the problem. It should be

(log√125 + log √27 - √8)/ (log 15 - log 2 )= 3/2.

ehild

13. Nov 16, 2012

### Mentallic

Re: Logs

Yes that's correct

No, again, you want to simplify that expression into a simple answer of 3/2, so what you're aiming to do is to combine each log term, not split them up further. Use the $\log(a)+\log(b)=\log(ab)$ rule.

Nope the $\sqrt{8}$ should be $\log(\sqrt{8})$

14. Nov 17, 2012

### lionely

Re: Logs

I still don't get it combine them? But aren't they too big? shouldn't I try to get them down to like small numbers and then try to cancel out?

15. Nov 17, 2012

### Mentallic

Re: Logs

Yes, combine them! If you get them down to small numbers then you'll end up with the fraction you posted earlier that cannot be cancelled further.

Use

$$\log(a)+\log(b)-\log(c)=\log\left(\frac{ab}{c}\right)$$

for both the numerator and denominator and see if you notice any nice cancellations.

16. Nov 17, 2012

### SammyS

Staff Emeritus
Re: Logs

Looks like a typo.

How about the first one should be:

(log√125 + log √27 - log√8)/ (log 15 - log 2 )= 3/2

As ehild said early on, you need to use sufficient parentheses .

17. Nov 17, 2012

### lionely

Re: Logs

thank you guys.