Embarrassing Precal Question

[poppe]

Hello,

I'm helping my girlfriend with a precal assignment. It is such an embarrassing problem since the problem is quite simple. I am curious if you all could help me. The book she is using is horrendous and does not explain anything that she needs to know (I've already taken calculus and crap).

Equation:

5 ^ (1-2x) = 1/5th

^ means "to the power of"

If you could just help me refresh my memory since it's been a little over a year now since I have taken any hard core math...

 

[swiftaw]

I presume you are trying to solve for x.

Well 1/5th is 5^(-1) thus (1-2x) = -1 thus x=1

Hello,

I'm helping my girlfriend with a precal assignment. It is such an embarrassing problem since the problem is quite simple. I am curious if you all could help me. The book she is using is horrendous and does not explain anything that she needs to know (I've already taken calculus and crap).

Equation:

5 ^ (1-2x) = 1/5th

^ means "to the power of"

If you could just help me refresh my memory since it's been a little over a year now since I have taken any hard core math...

 

[EricNau]

I believe the answer is (highlight for answer): x=1

If you multiply natural log by both sides, you can move the exponent to the front, like this:

(1-2x) log5 = log(1/5)​

Then you divide log5 on both sides, getting:

1-2x = [log(1/5)/log5]​

...Then you use a calculator to solve the logs, which gives you:

1-2x = -1​

Then you finish with basic algebra.


EDIT: I always was slow at math.

 

[swiftaw]

Then you divide log5 on both sides, getting:

1-2x = [log(1/5)/log5]​

...Then you use a calculator.

Or, remember that log(1/5) = log 1 - log 5 = 0 - log 5 = -log 5

Thus, 1-2x = -log 5 / log 5 = -1

And thus x = 1

 

[poppe]

I believe the answer is (highlight for answer): x=1

If you multiply natural log by both sides, you can move the exponent to the front, like this:

(1-2x) log5 = log(1/5)​

Then you divide log5 on both sides, getting:

1-2x = [log(1/5)/log5]​

...Then you use a calculator to solve the logs, which gives you:

1-2x = -1​

Then you finish with basic algebra.


EDIT: I always was slow at math.

Then you divide log5 on both sides, getting:

1-2x = [log(1/5)/log5]​

...Then you use a calculator.

Or, remember that log(1/5) = log 1 - log 5 = 0 - log 5 = -log 5

Thus, 1-2x = -log 5 / log 5 = -1

And thus x = 1

Can't use calculators....

I presume you are trying to solve for x.

Well 1/5th is 5^(-1) thus (1-2x) = -1 thus x=1

Oh man... so simple... Damn....

Now I'm already stuck on the next problem. I wish you could see this book... the only example equation for the whole book on this particular subject is 3^(x+1) = 81 and another problem that would be hard to make it clear since I can't write it out, but very very little explanations and help to guide you to the harder problems...

 

[swiftaw]

Can't use calculators....

Neither of my answers required a calculator

 

[iAlan]

The answer is 1







But I cheated and looked at the other members answers!
I can't even get my avatar right!

 

[EricNau]

Or, remember that log(1/5) = log 1 - log 5 = 0 - log 5 = -log 5

Thus, 1-2x = -log 5 / log 5 = -1

And thus x = 1

You're right, I had forgotten about that!

If I had known that calculators weren't allowed I probably would've looked a little harder for an easy way to solve it.

Thanks.

 

[poppe]

Neither of my answers required a calculator

Sorry I wasn't quoting your. The poster above your quote said use your calculator and I was just explaining that she can't use her calculator.

Thanks guys... I think I'm gonna have to whip out my old Trig book and see if I can help her better (that is if the assignment isn't due soon)

 

[swiftaw]

Sorry I wasn't quoting your. The poster above your quote said use your calculator and I was just explaining that she can't use her calculator.

No problemo

 

[siurpeeman]

i love answering these questions, but i usually go on macrumors late at night when these questions have already been answered. i know, i'm lame.

Now I'm already stuck on the next problem. I wish you could see this book... the only example equation for the whole book on this particular subject is 3^(x+1) = 81 and another problem that would be hard to make it clear since I can't write it out, but very very little explanations and help to guide you to the harder problems...

you could write out the equation on grapher, take a snapshot and post the image. an example would look like the following:

 

[poppe]

i love answering these questions, but i usually go on macrumors late at night when these questions have already been answered. i know, i'm lame.

you could write out the equation on grapher, take a snapshot and post the image. an example would look like the following:

We have a program called Grapher? well I'll be damn. Hey I still have 10 more problems if you want to do them (as long as you show me how to do them) Other wise my gal is just turning the 10 in not done.

 

[siurpeeman]

We have a program called Grapher? well I'll be damn. Hey I still have 10 more problems if you want to do them (as long as you show me how to do them) Other wise my gal is just turning the 10 in not done.

i'm sure if i don't, someone will.

 

[poppe]

i'm sure if i don't, someone will.

Sounds good.

 

[Eraserhead]

3^(x+1)=81

As 81=3^4

so by powers as before this says that:
x+1=4

So therefore.

x=3

get her another decent book on the subject (all Maths is the same so there's no harm), look at the reviews on Amazon, they should help you find if they are any good...

LATE EDIT: Basically with these problems try and turn one number on the bottom into a power of the other, then you can use (relatively) simple maths to find the answer.

 

[poppe]

Sorry for Double Post

More

 

[poppe]

3^(x+1)=81

As 81=3^4

so by powers as before this says that:
x+1=4

So therefore.

x=3

get her another decent book on the subject (all Maths is the same so there's no harm), look at the reviews on Amazon, they should help you find if they are any good...

I'm giving her my Trig book when I get back to my house. It was everything she's done in PreCal so far but with a million more explanations and demonstrations.

 

[siurpeeman]

four has a base of two, so you want to change the base to reflect that. once the bases are the same (2), you set the exponents equal. then you just solve.

 

[poppe]

Last Post

Whats worse than the book itself and it being so crappy is that her teacher, when she (along with other students) ask him a question the teacher would respond: If you don't know you probably shouldn't be in this class.

 

[siurpeeman]

all these problems are pretty much the same. all the numbers that you see have a common base. for example, numbers like 2, 4, 8, 16, 32 all have a base of 2. 3, 9, 81, and such have a base of 3. take these numbers and reduce to the common base. it's the best way to solve.

 

[poppe]

all these problems are pretty much the same. all the numbers that you see have a common base. for example, numbers like 2, 4, 8, 16, 32 all have a base of 2. 3, 9, 81, and such have a base of 3. take these numbers and reduce to the common base. it's the best way to solve.

Oh man.... Now this is all coming back... I can't believe I forgot these problems of all problems... Thanks a lot for all this help. This is helping so much!!!

 

[siurpeeman]

now i'm not going to do all of them, as they're all pretty much variations of the same problem. but i think you can get the general idea of what to do from here on out. if your gf is a college student, i imagine her school would offer free tutuoring on campus to help her with this sort of thing. maybe you/she could look into it. good luck!

btw, it's almost 4:30 in the morning. i take no responsibility for any mistakes in my work.

 

[furious]

all these problems are pretty much the same. all the numbers that you see have a common base. for example, numbers like 2, 4, 8, 16, 32 all have a base of 2. 3, 9, 81, and such have a base of 3. take these numbers and reduce to the common base. it's the best way to solve.

Why are you not my Teacher. I do quants and we did differentiation. Boy is it hard. Having only do general math is high school. You can guess how much I suck at math.

 

[poppe]

now i'm not going to do all of them, as they're all pretty much variations of the same problem. but i think you can get the general idea of what to do from here on out. if your gf is a college student, i imagine her school would offer free tutuoring on campus to help her with this sort of thing. maybe you/she could look into it. good luck!

btw, it's almost 4:30 in the morning. i take no responsibility for any mistakes in my work.

Hey thanks so much! She is getting tutoring (or so she tells me) She let her 2 Biology classes and her 2 Biology Labs take over in priority so Math came last and well now... she has screwed herself for tomorrow's homework, well that was until you guys all helped. Thank you all so much!!!!


EDIT: Just to let you all know. I have worked the remainder and have gotten them all done. thank you so much again.

 

[MongoTheGeek]

When in doubt the answer is 0,1,-1 or if it involves circles pi.