Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#126 2013-07-23 23:31:39

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

I think 5 is raising to the power nothing therefore should be equal to  zero and not one.


I know only one thing - that is that I know nothing

Offline

#127 2013-07-23 23:31:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

Supposing you had

2^4 * 2^0

when we multiply the same bases we are allowed to add the exponents.  4 + 0 = 4 so 2^4 * 2^0 = 2^4 so 2^0 must equal 1.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#128 2013-07-23 23:44:23

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

But is it possible to add the exponents of the following? 

Last edited by EbenezerSon (2013-07-23 23:45:13)


I know only one thing - that is that I know nothing

Offline

#129 2013-07-23 23:51:03

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

No, it is not. They do not have the same base.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#130 2013-07-24 00:06:56

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

It is due to such situations why I could not solve the previous problem since it has 6*3^2n+3. the six made it hard for me to manipulate. One cannot reduce it to be three. Or if the six had been three I would multiply it with the three to get nine and then reduce it to three, so I could manipulate. Since nine would be a perfect square.


I know only one thing - that is that I know nothing

Offline

#131 2013-07-24 00:09:25

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

Then the final answer would be 9*16 = 144, is that right?


I know only one thing - that is that I know nothing

Offline

#132 2013-07-24 00:11:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

6 = 2 * 3 so you could have combined that statement into

6*3^(2n+3) = 2 *3 * 3^(2n+3)=  2 * 3^(2n+4)

and you are done.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#133 2013-07-24 00:19:52

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

bobbym wrote:

6 = 2 * 3 so you could have combined that statement into

6*3^(2n+3) = 2 *3 * 3^(2n+3)=  2 * 3^(2n+4)

and you are done.

I don't understand yours, I thought it would be

2*3*3(2n+3) = 2*9^(2n+3) = 2*3^3(2n+3) = 2*3^(6n+9)

Last edited by EbenezerSon (2013-07-24 00:20:56)


I know only one thing - that is that I know nothing

Offline

#134 2013-07-24 00:24:35

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

I must review your procedure with the previous problem to comprehend.


I know only one thing - that is that I know nothing

Offline

#135 2013-07-24 00:25:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

You add coefficients:

2 * 3^1 * 3^(2n+3)

2n +3 + 1 = 2n + 4 so

2 * 3^(2n+4)

Are you saying that

because that is incorrect.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#136 2013-07-24 00:30:16

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

Errrr okay I have got you, then what would one  make of the two, I mean the base.

Last edited by EbenezerSon (2013-07-24 00:33:59)


I know only one thing - that is that I know nothing

Offline

#137 2013-07-24 00:35:55

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

bobbym wrote:

You add coefficients:

2 * 3^1 * 3^(2n+3)

2n +3 + 1 = 2n + 4 so

2 * 3^(2n+4)

Are you saying that

because that is incorrect.

The two I have underlined above.


I know only one thing - that is that I know nothing

Offline

#138 2013-07-24 00:37:49

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

Hi;

You can only do this:


6 * 3^(2n+3)

2 * 3 * 3^(2n+3)

2 * 3^1 * 3^(2n+3)

Add the exponents on the threes.

2n +3 + 1 = 2n + 4 so

2 * 3^(2n+4)


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#139 2013-07-24 00:43:17

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

Okay I digest it. But can I  use that procedure to arrive on that answer 7 you had in the previous problem?

Last edited by EbenezerSon (2013-07-24 00:44:58)


I know only one thing - that is that I know nothing

Offline

#140 2013-07-24 00:46:04

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

That problem is a real bear and I recommend the other method, the one I posted.

I am going to get a little bit of sleep see you later.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#141 2013-07-24 00:49:48

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

Okay,  Thanks God bless. I shall solve more problems.


I know only one thing - that is that I know nothing

Offline

#142 2013-07-24 02:43:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

How did you do?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#143 2013-07-24 03:52:01

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

Hi, bobbym I have come across another confusing one with different bases.

Solve for X.

3^x * 2^x-1 = 1.

How would one go about this? Is wierd.

Last edited by EbenezerSon (2013-07-24 04:01:51)


I know only one thing - that is that I know nothing

Offline

#144 2013-07-24 03:53:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

Is that

because if it is...


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#145 2013-07-24 04:36:19

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

The book has 0.39 answer


I know only one thing - that is that I know nothing

Offline

#146 2013-07-24 04:43:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

That is correct if you round my answer to 2 decimal places.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#147 2013-07-24 06:58:42

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

bobbym wrote:

Is that

because if it is...

Please help me understand this.

Thanks in advance


I know only one thing - that is that I know nothing

Offline

#148 2013-07-24 14:58:41

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

I can show you the steps but unless you have a little knowledge about logarithms it will be confusing.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

#149 2013-07-24 20:46:43

EbenezerSon
Member
Registered: 2013-07-04
Posts: 456

Re: Simplify the following:

I had solved much problems on logarithms.
Usually I had encountered problems on indices with unequal bases, and the book used log to solve but I can't percieve this would need logarithm application.

Please carry on!


I know only one thing - that is that I know nothing

Offline

#150 2013-07-24 20:56:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,300

Re: Simplify the following:

Okay, I will provide the steps:

Take the log of both sides.

Add log(2) to both sides.

Divide both sides by ( log(2) + log(3) ).

And we are done.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

Online

Board footer

Powered by FluxBB