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paulb203

Member

Registered: 2023-02-24

Posts: 321

Exponents / Algebra / Equations

bx^6 = (3x^2)^c

First off;

How to tackle (3x^2)^c?

If c was, say, 2, then we would have; (3x^2)(3x^2), yeah?

Which would = 9x^4, yeah?

Can we do; (3x^2)^c = 3x^2*c? (multiply the exponents, 2*c)

Which would, if c was 2, = 3x^4

No? Because we already got = 9x^4?

*

And then with the whole equation; what can we do to both sides?

The only thing I can think of is to divide both sides by b, but that looks awkward - making the right hand side a fraction with b on the bottom!

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Prioritise. Persevere. No pain, no gain.

KerimF

Member

From: Aleppo-Syria

Registered: 2018-08-10

Posts: 248

Re: Exponents / Algebra / Equations

To avoid confusion or for clarity, I used to add '*' always to denote a product.
For example
bx^6 = (3x^2)^c becomes:
b*(x^6) = [3*(x^2)]^c

Now we can also write it as:
b*(x^6) = (3^c)*[(x^2)]^c
b*(x^6) = (3^c)*[x^(2*c)]
etc...

Last edited by KerimF (2024-05-16 09:57:51)

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Every living thing has no choice but to execute its pre-programmed instructions embedded in it (known as instincts).
But only a human may have the freedom and ability to oppose his natural robotic nature.
But, by opposing it, such a human becomes no more of this world.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Exponents / Algebra / Equations

bx^6 = (3x^2)^c

What are we meant to do with this expression?

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Exponents / Algebra / Equations

bx^6 = (3x^2)^c

What are we meant to do with this expression?

Bob

I asked myself that very same question.

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Exponents / Algebra / Equations

To avoid confusion or for clarity, I used to add '*' always to denote a product.
For example
bx^6 = (3x^2)^c becomes:
b*(x^6) = [3*(x^2)]^c

Now we can also write it as:
b*(x^6) = (3^c)*[(x^2)]^c
b*(x^6) = (3^c)*[x^(2*c)]
etc...

Thanks, KerimF

---

Prioritise. Persevere. No pain, no gain.

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Exponents / Algebra / Equations

bx^6 = (3x^2)^c

What are we meant to do with this expression?

Bob

Doh! I forgot to add the crucial part; find out the value of b, and the value of c.

---

Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Exponents / Algebra / Equations

I thought I was missing something

As x can anything you can equate the non x bits and separately the x bits

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Exponents / Algebra / Equations

Thanks, Bob

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Prioritise. Persevere. No pain, no gain.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Exponents / Algebra / Equations

I thought I was missing something

As x can anything you can equate the non x bits and separately the x bits

Bob

Nicely-done!

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Exponents / Algebra / Equations

"As x can anything you can equate the non x bits and separately the x bits"

x is a variable, yeah?

Are b and c not variables? Can they not be anything?

I know you've shown them to be 27,3, here, but how do I know when first looking at the problem that b and c are different from x (in terms of the latter being able to be anything)?

Is there no permuation of values where b and c could equal something different?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,627

Re: Exponents / Algebra / Equations

I get what you're saying but I don't think so.  From the wording b and c have values we can compute whereas x is truely a variable in the sense that, once you have computed b and c, the equation has to hold true whatever value x takes.

Like the circle question this is something I've always accepted and used without questioning it.  I like that you do question it; that's the mark of a true mathematician.  So now I'll have to think up a proof for paragraph 1.

LATER EDIT:

Substitute some values:

x = 1    =>    b = 3^c   .........equation a

x = 2    =>    64b= (3 times 4)^c = 3^c times 4^c  .........equation b

Substitute a into b =>  64b = b times 4^c     =>   4^c = 64   =>   c = 3

=>   b = 27

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 321

Re: Exponents / Algebra / Equations

Thanks a lot, Bob.

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Prioritise. Persevere. No pain, no gain.

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Exponents / Algebra / Equations

I get what you're saying but I don't think so.  From the wording b and c have values we can compute whereas x is truely a variable in the sense that, once you have computed b and c, the equation has to hold true whatever value x takes.

Like the circle question this is something I've always accepted and used without questioning it.  I like that you do question it; that's the mark of a true mathematician.  So now I'll have to think up a proof for paragraph 1.

LATER EDIT:

Substitute some values:

x = 1    =>    b = 3^c   .........equation a

x = 2    =>    64b= (3 times 4)^c = 3^c times 4^c  .........equation b

Substitute a into b =>  64b = b times 4^c     =>   4^c = 64   =>   c = 3

=>   b = 27

Bob

Another great reply and effort. We need more people like Bob here.