# Properties of exponents and logs problem

1. Sep 19, 2009

### fatcrispy

Find B when given: Y = log2B and 2y+4 + 4y+3 = 224

I could use some help figuring out the process to this. Thanks

2. Sep 19, 2009

### rock.freak667

Re: Logs

the log of a number is the power to which the base is raised to give that number

so if z=ab then b=logaz

3. Sep 20, 2009

### fatcrispy

Re: Logs

I'm still having trouble. 2y=z and y+4=log2Z and y+3=log4R? What do I do with this? Could you help me solve it please I am kind of lost.

I get Z + R = 224 and B = 2Y Now what?

4. Sep 20, 2009

### Bohrok

Re: Logs

You need to remember some properties of exponents:

xa+b = xa·xb
xab = (xa)b

Also, it can help to rewrite 4 as 22.

When you can rewrite the equation with 2y, replace them with B and then solve for B.

5. Sep 20, 2009

### fatcrispy

Re: Logs

Ok so I got a funky answer.

2y24+22y26=224
B=2y So,
16B+64B2=224
4B2+B=14

I ended up with B=-2 but that doesn't make sense with -2=2y

6. Sep 20, 2009

### Bohrok

Re: Logs

That's only one (extraneous) root of the quadratic equation you got. The other one is the correct answer.

7. Sep 20, 2009

### fatcrispy

Re: Logs

Ah 7/4 thanks!