# Thread: Find solutions to logs

1. ## Find solutions to logs

I have two problems, which I'd like to put into its own thread. WolframAlpha gives me weird solutions to both of these problems.

1)

I'm at a complete loss as in doing this problem .

2)

AFAIK, I can use a algebraic property of log to combine parts of the equation:

If that was correct, then I don't know what to do from there. If it isn't correct, then I still don't know what to do from there.

2. Originally Posted by BeSweeet
I have two problems, which I'd like to put into its own thread. WolframAlpha gives me weird solutions to both of these problems.

1)

I'm at a complete loss as in doing this problem .

2)

AFAIK, I can use a algebraic property of log to combine parts of the equation:

If that was correct, then I don't know what to do from there. If it isn't correct, then I still don't know what to do from there.
The algebraic property of logarithms that you referred to is:

$log(a) + log(b) = log(ab) \Rightarrow log(x) + log(x-8) = log(x(x-8)) = log(x^2-8x)$

As for the first:

Let $t=2^x$. Remember that $2^{-x} = \frac{1}{2^x} \Rightarrow \frac{1}{t} = 2^{-x}$

So we have: $t + \frac{12}{t} - 7 = 0 \Rightarrow t^2 + -7t +12 = 0 \Rightarrow$ $t_{1,2} = \frac{7 \pm \sqrt{49-4\cdot (12)}}{2} = \frac{7 \pm 1}{2} = 4,3$

So we got $t=4,3 \Rightarrow 2^x = 4,3 \Rightarrow x = log_{2}(4), log_{2}(3)$

Substitute both these values into the original equation and see if they fit.

3. Originally Posted by Defunkt
The algebraic property of logarithms that you referred to is:

$log(a) + log(b) = log(ab) \Rightarrow log(x) + log(x-8) = log(x(x-8)) = log(x^2-8x)$
...

Either way, I don't know what to do...

4. Originally Posted by BeSweeet
...

Either way, I don't know what to do...
$e^{log(x^2-8x)} = e^2$

Can you solve now, using the definition of log?

5. Originally Posted by Defunkt
$e^{log(x^2-8x)} = e^2$

Can you solve now, using the definition of log?
I can't .