Thread: Stuck on a Log :(

1. Stuck on a Log :(

Here is what i have thus far..

2^(3x-4) -3^(2x+5) = 7
3xlog2 -4log2 +2xlog-3 +5log-3 = 7
3xlog2 +2xlog-3 = 7 + 4log2 -5log-3
3xlog2+ 2xlog-3 = 7 +log256 - log 243
3xlog2+ 2xlog-3 = 7 + log(256/243)
3xlog2+ 2xlog-3 = 8.05

Not sure where to take it from here. Any help is appreciated <3.

2. You calculated the log values on the right hand side, so why can't you do it on the left hand side? Also, you never took the log of the seven in the first line. BTW, you cannot take the log of a negative number...

$\displaystyle 2^{(3x-4)} -3^{(2x+5)} = 7$

$\displaystyle (3x-4)log(2) -(2x+5)log(3) = log(7)$

Calculate the value of those logs, and then solve for x.

3. Ah, thanks. Yea.. im not actually sure how to isolate the x's on the left side and I cant find my note on it :|. Ive got it down to..

3xlog2 -2xlog3 = 7.37

4. Originally Posted by BrendanS
Ah, thanks. Yea.. im not actually sure how to isolate the x's on the left side and I cant find my note on it :|. Ive got it down to..

3xlog2 -2xlog3 = 7.37
$\displaystyle log(2)=.301$, $\displaystyle log(3)=.477$

$\displaystyle .903x-.954x=7.37$

$\displaystyle x=-143.83$

This is correct given that the right side (7.37) was correctly done.

5. Thanks your a life saver <3, last day before exams start and im the only one that showed up for class with a single question >_> .

6. Originally Posted by colby2152
$\displaystyle 2^{(3x-4)} -3^{(2x+5)} = 7$

$\displaystyle (3x-4)log(2) -(2x+5)log(3) = log(7)$
Careful with this step.

Recall $\displaystyle \log(a-b)$ has not property.

7. Originally Posted by Krizalid
Careful with this step.

Recall $\displaystyle \log(a-b)$ has not property.
What do you mean? Yes, you cannot take the log of the negative number, but you can switch it to the right side and do the same calculation.

8. Originally Posted by colby2152
What do you mean? Yes, you cannot take the log of the negative number
I never spoke about logs of negative numbers.

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What you did here

Originally Posted by colby2152
$\displaystyle 2^{(3x-4)} -3^{(2x+5)} = 7$

$\displaystyle (3x-4)log(2) -(2x+5)log(3) = log(7)$
It is incorrect, 'cause $\displaystyle \log (a - b) \ne \log a - \log b.$

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I suggest to make a graph of the equation.

9. True true.. brain fart there, thought I could do that because I am so used to working with $\displaystyle Ae^x=B$ forms.

10. Originally Posted by BrendanS
Here is what i have thus far..

2^(3x-4) -3^(2x+5) = 7
3xlog2 -4log2 +2xlog-3 +5log-3 = 7
3xlog2 +2xlog-3 = 7 + 4log2 -5log-3
3xlog2+ 2xlog-3 = 7 +log256 - log 243
3xlog2+ 2xlog-3 = 7 + log(256/243)
3xlog2+ 2xlog-3 = 8.05

Not sure where to take it from here. Any help is appreciated <3.
Hi,

$\displaystyle 2^{3x-4} -3^{2x+5} = 7~\iff~\frac1{16} \cdot 8^x - 243 \cdot 9^x = 7$

By comparison of the coefficients and the bases it follows that the LHS is negative. Thus this equation doesn't have a real solution.