## 8^2x+2 = 7^x-2

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
fancynancy80
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### 8^2x+2 = 7^x-2

I am having a problem with this homework problem. I have asked my teacher to help but she wont respond for 3 days or so. Anyway, I have gotten this problem wrong and a new one has generated. the answer to the problem was -3.6380
The biggest issue I have with this problem is the end when you must condense everything. I can get it down to -2ln8-2ln7/2ln8-ln7 I just dont know what to make the -2
Is it turned into ln8^-2 or ln8^1/2 I know these are wrong, that is why I need help.

Martingale
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### Re: 8^2x+2 = 7^x-2

fancynancy80 wrote:I am having a problem with this homework problem. I have asked my teacher to help but she wont respond for 3 days or so. Anyway, I have gotten this problem wrong and a new one has generated. the answer to the problem was -3.6380
The biggest issue I have with this problem is the end when you must condense everything. I can get it down to -2ln8-2ln7/2ln8-ln7 I just dont know what to make the -2
Is it turned into ln8^-2 or ln8^1/2 I know these are wrong, that is why I need help.

is this

$8^{2x+2}=7^{x-2}$

the equation?

fancynancy80
Posts: 6
Joined: Tue Apr 19, 2011 5:16 pm
Contact:

### Re: 8^2x+2 = 7^x-2

Yes that is correct.

Martingale wrote:
fancynancy80 wrote:I am having a problem with this homework problem. I have asked my teacher to help but she wont respond for 3 days or so. Anyway, I have gotten this problem wrong and a new one has generated. the answer to the problem was -3.6380
The biggest issue I have with this problem is the end when you must condense everything. I can get it down to -2ln8-2ln7/2ln8-ln7 I just dont know what to make the -2
Is it turned into ln8^-2 or ln8^1/2 I know these are wrong, that is why I need help.

is this

$8^{2x+2}=7^{x-2}$

the equation?

Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

### Re: 8^2x+2 = 7^x-2

fancynancy80 wrote: I can get it down to -2ln8-2ln7/2ln8-ln7

that is the correct answer (provided you put it in parentheses)

(-2ln8-2ln7)/(2ln8-ln7)

fancynancy80
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### Re: 8^2x+2 = 7^x-2

no it wanted the calculator total that was supposed to come to -3.6380 You are supposed to condense the problem down, something like this
ln8^-2 - ln7^2/ln8^2 - ln7
only the ^-2 part is wrong, that is were I need help, figuratively speaking you would then do the next part, which is to use all the powers.
ln8^-2 would be = ln 0.015625 (wrong I know but I did say figuratively)
ln7^2= ln 49
then the bottom part of the fraction would be
ln8^2= ln64
ln7 would remain the same.
then you would put it all back together and it would look something like this.
ln0.015625-ln49/ln64-ln7
then you wold take the top and divide the two then do the same with the bottom, and then you would be ready to put it into the calculator. I have no idea what I'm talking about really this is just what I sow on the "helpful" similar problem video that accompanies the homework problem. they pass steps though and those are usually the steps I need.

Martingale
Posts: 350
Joined: Mon Mar 30, 2009 1:30 pm
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### Re: 8^2x+2 = 7^x-2

fancynancy80 wrote:no it wanted the calculator total that was supposed to come to -3.6380 You are supposed to condense the problem down, something like this
ln8^-2 - ln7^2/ln8^2 - ln7
only the ^-2 part is wrong, that is were I need help, figuratively speaking you would then do the next part, which is to use all the powers.
ln8^-2 would be = ln 0.015625 (wrong I know but I did say figuratively)
ln7^2= ln 49
then the bottom part of the fraction would be
ln8^2= ln64
ln7 would remain the same.
then you would put it all back together and it would look something like this.
ln0.015625-ln49/ln64-ln7
then you wold take the top and divide the two then do the same with the bottom, and then you would be ready to put it into the calculator. I have no idea what I'm talking about really this is just what I sow on the "helpful" similar problem video that accompanies the homework problem. they pass steps though and those are usually the steps I need.

hmmm..not really sure what you are trying to accomplish here since you already have the answer...but...

$=\frac{-2\ln(8)-2\ln(7)}{2\ln(8)-\ln(7)}$

$=\frac{\ln(8^{-2})+\ln(7^{-2})}{\ln(8^2)-\ln(7)}$

$=\frac{\ln\left(8^{-2}7^{-2}\right)}{\ln\left(\frac{8^2}{7}\right)$

$=\frac{\ln\left(56^{-2}\right)}{\ln\left(\frac{64}{7}\right)$

=... you could do more if you wanted to

fancynancy80
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### Re: 8^2x+2 = 7^x-2

This is the link to the video I was talking about, I don't know if it will open for you, but its worth a try.
http://www.mathxl.com/Student/MediaPopu ... terwin=yes

fancynancy80
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### Re: 8^2x+2 = 7^x-2

fancynancy80 wrote:This is the link to the video I was talking about, I don't know if it will open for you, but its worth a try.
http://www.mathxl.com/Student/MediaPopu ... terwin=yes

Well poops, its doesn't work. I will try a differnt way. like I said its not the same problem but it is sort of like it.

fancynancy80
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Joined: Tue Apr 19, 2011 5:16 pm
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