Simplify the following:

EbenezerSon · 2013-07-23 23:31:39

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

bobbym · 2013-07-23 23:31:49

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.

EbenezerSon · 2013-07-23 23:44:23

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

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

bobbym · 2013-07-23 23:51:03

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

EbenezerSon · 2013-07-24 00:06:56

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.

EbenezerSon · 2013-07-24 00:09:25

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

bobbym · 2013-07-24 00:11:10

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.

EbenezerSon · 2013-07-24 00:19:52

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)

EbenezerSon · 2013-07-24 00:24:35

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

bobbym · 2013-07-24 00:25:02

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.

EbenezerSon · 2013-07-24 00:30:16

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)

EbenezerSon · 2013-07-24 00:35:55

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.

bobbym · 2013-07-24 00:37:49

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)

EbenezerSon · 2013-07-24 00:43:17

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)

bobbym · 2013-07-24 00:46:04

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.

EbenezerSon · 2013-07-24 00:49:48

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

bobbym · 2013-07-24 02:43:47

How did you do?

EbenezerSon · 2013-07-24 03:52:01

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)

bobbym · 2013-07-24 03:53:51

Is that

because if it is...

EbenezerSon · 2013-07-24 04:36:19

The book has 0.39 answer

bobbym · 2013-07-24 04:43:12

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

EbenezerSon · 2013-07-24 06:58:42

bobbym wrote:

Is that
because if it is...

Please help me understand this.

Thanks in advance

bobbym · 2013-07-24 14:58:41

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

EbenezerSon · 2013-07-24 20:46:43

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!

bobbym · 2013-07-24 20:56:55

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.

Math Is Fun Forum

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

Re: Simplify the following:

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

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

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

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