Exponential equations and logarithms

nanana

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Hi! I need some help with exponential equations and logarithms.The following exercises were on my test ,but I wasn't able to resolve most of them (our teacher made some of us re-take the exam since she thought we cheated ,but she increased the difficulty ) .I know that I am not supposed to post more than one exercise,but I didn't want to spam the forum with multiple ones...if necessary I will post them separately .

Math.jpg
It would be great if you could help me doing one or two.Have a good day!
nanana
 
Hi! I need some help with exponential equations and logarithms.The following exercises were on my test ,but I wasn't able to resolve most of them (our teacher made some of us re-take the exam since she thought we cheated ,but she increased the difficulty ) .I know that I am not supposed to post more than one exercise,but I didn't want to spam the forum with multiple ones...if necessary I will post them separately .

View attachment 10685
It would be great if you could help me doing one or two.Have a good day! nanana
You did not tell us what you are being asked in each of the questions (and exactly where you are getting stuck!)
 
Hi! I need some help with exponential equations and logarithms.The following exercises were on my test ,but I wasn't able to resolve most of them (our teacher made some of us re-take the exam since she thought we cheated ,but she increased the difficulty ) .I know that I am not supposed to post more than one exercise,but I didn't want to spam the forum with multiple ones...if necessary I will post them separately .

View attachment 10685
It would be great if you could help me doing one or two.Have a good day!
nanana
Please read

https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=433156&viewfull=1#post433156

We do not view posting multiple problems as spam, but we greatly prefer that each problem be in its own thread. Answering multiple questions in one thread quickly becomes VERY confusing to everyone.

And as you will see when you have read the summary of the guidelines, we need information about what you have tried by showing your work or, at the very least, an explanation of why you cannot even start to work.
 
Please read

https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=433156&viewfull=1#post433156

We do not view posting multiple problems as spam, but we greatly prefer that each problem be in its own thread. Answering multiple questions in one thread quickly becomes VERY confusing to everyone.

And as you will see when you have read the summary of the guidelines, we need information about what you have tried by showing your work or, at the very least, an explanation of why you cannot even start to work.

Sorry for the trouble;as soon as possible I will post every problem separately and show what I have done.
 
I have trouble reading your attachment.

Is the first problem to solve for x given

\(\displaystyle \dfrac{\sqrt{2^{(x-2)}} + \sqrt{2^{(6-x)}}}{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}} = \dfrac{7}{4}.\)

Is that REALLY the problem?

\(\displaystyle \dfrac{\sqrt{2^{(x-2)}} + \sqrt{2^{(6-x)}}}{\sqrt{2^{(6-x)}}+ \sqrt{2^{(x-2)}}} = \dfrac{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}}{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}} = 1 \ne \dfrac{7}{4}.\)

There is no value of x that satisfies that equation.
 
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I have trouble reading your attachment.

Is the first problem to solve for x given

\(\displaystyle \dfrac{\sqrt{2^{(x-2)}} + \sqrt{2^{(4-x)}}}{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}} = \dfrac{7}{4}.\)

Is that REALLY the problem?

\(\displaystyle \dfrac{\sqrt{2^{(x-2)}} + \sqrt{2^{(6-x)}}}{\sqrt{2^{(6-x)}}+ \sqrt{2^{(x-2)}}} = \dfrac{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}}{\sqrt{2^{(6-x)}} + \sqrt{2^{(x-2)}}} = 1 \ne \dfrac{7}{4}.\)

There is no value of x that satisfies that equation.
JeffM, I read what you noted as 6 in the numerator as a 4
 
JeffM, I read what you noted as 6 in the numerator as a 4
Thanks jomo.

One of the problems with getting old is that I do not see well.

In any case, if students insist on giving a problem in jpegs, they should make sure that they render clearly.
 
Sorry for the trouble;as soon as possible I will post every problem separately and show what I have done.
If you intend to "show" by using pictures of your work,
PLEASE write clearly and carefully.
 
Okay. I've played with this and can't find a solution either. (Neither does my version of Mathematica.)

However, I've a tiny suspicion there might be a complex solution. There is apparently a glitch in my derivation because I can't make it fit the original equation. But I can't help the feeling there is the log of a negative number involved. I'll play with it.

-Dan
 
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