# Log problem

1. Jul 27, 2008

### yoleven

1. The problem statement, all variables and given/known data
If logb(2)=0.4307, find logb(16)

2. Relevant equations

3. The attempt at a solution
If the log has the same base can I eliminate it and solve the equation?
If b^.04307=2 then b^?=16
can I say 2/.04307=16/x
16*0.4307=2x
x=3.4456
Am I close or have I missed something obvious?

2. Jul 27, 2008

### tiny-tim

NO!

Hint: 16 = 2 x 2 x 2 x 2.

3. Jul 27, 2008

### yoleven

Okay, 2^4=16
If I have b^.4307=2 By trial and error, I came up with 5 for b. 5^.4307=2 or log5(.4307)=2
Specifically, what steps do I follow to discover what the base is without resorting to a trial and error method.
Thanks

4. Jul 27, 2008

### Avodyne

Start with b^.4307=2, and raise both sides to a certain power, such that you will get 16 on the right.

5. Jul 28, 2008

### tiny-tim

Hi yoleven!

You don't need to find b … the question doesn't ask you for b.

Hint: 16 = 2 x 2 x 2 x 2.

logb(pq) = logb(p) + logb(q)

6. Jul 28, 2008

### HallsofIvy

Staff Emeritus
Or, more simply for this problem log(ab)= b log(a).

7. Jul 28, 2008

### tiny-tim

oooh … that's far too advanced!

8. Jul 28, 2008

### yoleven

If logb(2)=.4307
logb(16)=1.7228
because if b^.4307=2, (b^.4307)^4=(2)^4
b^1.7228=16
Okay? Thanks again.

9. Jul 28, 2008

### FordPrefect

1.7228 is correct.