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Indices - Went Wrong And Don't Know Why?

I have the question 'solve 3^x x 9^x = root 3'
I took the following steps:
3^x x (3^2)^x = root 3
(then divided by 3)
x x 2x = root 1
I stopped at 2x^2 = root 1, because I figured I'd used a wrong method.
Can anybody explain?

Thank you
Original post by TeacupAndTragedy
I have the question 'solve 3^x x 9^x = root 3'
I took the following steps:
3^x x (3^2)^x = root 3
(then divided by 3)
x x 2x = root 1
I stopped at 2x^2 = root 1, because I figured I'd used a wrong method.
Can anybody explain?

Thank you

3x×9x=33^x \times 9^x =\sqrt 3
Original post by TeacupAndTragedy
I have the question 'solve 3^x x 9^x = root 3'
I took the following steps:
3^x x (3^2)^x = root 3
(then divided by 3)
x x 2x = root 1
I stopped at 2x^2 = root 1, because I figured I'd used a wrong method.
Can anybody explain?

Thank you


root 3 divided by 3 isn't root 1 i don't think

combine 3xand 32x3^x and\ 3^{2x}

i'd then suggest squaring everything to get rid of that square root because no-one likes square roots lol
3^x divided by 3 doesnt equal x...it equals 3^(x-1)

what you should do is put root 3 into an index and then all the expressions will be 3 to the power of something. that means that you can add the powers on the left side (because youre timesing the expressions) and that will equal the power on the right side
Original post by hpblcparaboloid
3^x divided by 3 doesnt equal x...it equals 3^(x-1)

what you should do is put root 3 into an index and then all the expressions will be 3 to the power of something. that means that you can add the powers on the left side (because youre timesing the expressions) and that will equal the power on the right side


So would that be:
3^x times (3^2)^x = 3^1/2
So 3x=1/2?
yes!
Original post by will'o'wisp2
root 3 divided by 3 isn't root 1 i don't think

combine 3xand 32x3^x and\ 3^{2x}

i'd then suggest squaring everything to get rid of that square root because no-one likes square roots lol


Nobody likes square roots aha!
Original post by hpblcparaboloid
yes!


Thanks!

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