Expoents

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Anonymous

Expoents 2016-01-17 17:30:12 Post No. 7790782

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Expoents 2016-01-17 17:30:12 Post No. 7790782

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Can you prove 3^x is equal to 3^(1-x) using only expoents rules?

You are not allowed to turn it into an equation

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>>7790782

>can you prove 3^x is equal to 3^(1-x) using only expoents rules?

Let x=0

3^0=1

3^(1-0)=3^1=3

1=/=3

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This doesn't even make sense

3^2=9, 3^(1-2)=1/3

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>>7790782

no...

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x=1/2

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This is possible the solution is 1/2. But I need to know how to solve it using only expoents rules. Dont make an equation out of it, making 3^x= 3^(1-x) is the easy way

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You cant just give out values to x. X only has one solution and that already was found out so dont say it doesnt make sense just because the solution is not what you want

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rule 2

rule 1 + 5

2x = 1

fill in gaps as necessary

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>>7790853

Checking it

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>>7790782

>prove 3^x is equal to 3^(1-x)

>prove

no one can because it is wrong

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>>7790853

Doesnt make sense

3^x = 0^x : 3^x wont get you to 3^(1-x)

Nor the other way around : 3^(1-x) = 3^1 : 3^x as this isnt nowhere near 3^x

None of the above work

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>>7790863

Its not wrong when x=1/2 therefore solution is 1/2. I dont think you can get to x using only the expoents rules

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>>7790896

I might have not been fully explicit. The exercise says that 3^(1-x)=6 and you have to take 3^x turn it into 3^(1-x) so you can replace it by 6 and calculate whatever expression you have so you can get 1/2

You should only do it using the rules and thats what Im having problems with

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>>7790920

so do you mean like 3^(1-x) = 3^1 * 3^(-x) = 3^1 * 1/3^x

now you have an expression containing 3^x so you can substitute.

that's how I would interpret the instructions.

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>>7791023

You interpreted it right the only problem is that you took the wrong expression. Do the same starting with 3^x

Take this example:

You know that 3^(1-x) = 6. The expression in the example is 3^(2-2x)

Solution:

3^(2-2x)= 3^((1-x)*2) [rule 3] = 6^2 = 36

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>>7791023

3^x = 3^(x-1+1) = 3^(x-1) * 3 = 1/3^(1-x) * 3

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>>7791155

Genius. Thanks, its exactly this

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>>7790874

What they mean is that it has been worded incorrectly.

A proof that 3^x is equal to 3^(1-x) is a proof that they are equal for ALL x. What should have been asked for is a solution to 3^x = 3^(1-x), or in words:

>Can you find the values of x for which 3^x is equal to 3^(1-x), using only these exponent rules?

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>>7791155

Where did that 1/3 come from?

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>>7791225

You're right. My mistake

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