# Homework Help: Exam problem : solve exponential withh log? This one is killin me

1. Jun 22, 2011

### sixshot8

exam problem : solve exponential withh ... log? This one is killin me!!

36^x-6*6^x=-9

2. Jun 22, 2011

### cepheid

Staff Emeritus
Re: exam problem : solve exponential withh ... log? This one is killin me!!

Welcome to PF sixshot8!

Remember that the logarithm to base "n" of something is the inverse operation of raising n to the power of that something i.e.:

logn(nx) = x

Now, you can rewrite every term on the left hand side as a power of 6:

36x = (62)x = ?

6*6x = 616x = ?

Use what you know about the rules of exponents to fill in the question marks.

So, it seems like at some point, taking a base 6 logarithm might be useful. Or you can express the exponentials in terms of another base, like 'e', that might be more convenient.

We don't do people's homework for them at PF, so I'm not going to give you a step by step solution.

EDIT: Looking at things more closely, I think it might be useful to express each term as a multiple of 6x

3. Jun 22, 2011

### eumyang

Re: exam problem : solve exponential withh ... log? This one is killin me!!

Similar to what cepheid originally said, make a substitution where w = 6x. Rewrite the original equation in terms of w, and go on from there.

4. Jun 23, 2011

### AJKing

Re: exam problem : solve exponential withh ... log? This one is killin me!!

$36^{x-6}*6^x = (-9)$

or

$36^{x}-6*6^x = (-9)$

I would think you mean the first, correct?

5. Jun 23, 2011

### Mentallic

Re: exam problem : solve exponential withh ... log? This one is killin me!!

The second seems more likely considering how often they like to bring up these kinds of questions.

6. Jun 23, 2011

### Skins

Re: exam problem : solve exponential withh ... log? This one is killin me!!

You have

$$36^{x}-6(6^{x}) = -9$$

which you can also write as

$$36^{x}\, -\, 6(6^{x}) \, + \,9=0$$

Now

$$36^{x} \, = \, (6.6)^{x} \, = \, (6^{2})^{x} \, = \, (6^{x})^{2}$$

So your above equation can be written as

(**) $$(6^{x})^{2} \, - \, 6(6^{x}) \, + \, 9 \, = \, 0$$

Does equation (**) seem to have a familiar (common) looking form that you have seen before ? Think about it. How would you go about solving for
$$6^{x}$$ ?

Last edited: Jun 23, 2011
7. Jun 23, 2011

### Redbelly98

Staff Emeritus
Re: exam problem : solve exponential withh ... log? This one is killin me!!

Moderator's note:

Now that the OP has received plenty of hints, let's wait for a response before offering further help.

8. Jun 23, 2011

### Staff: Mentor

Re: exam problem : solve exponential withh ... log? This one is killin me!!

Slightl;y OT, but I don't see how the first could give negative result.