exponential equation!!

[chutch82]

find the solution of the exponential equation:

3^2x= 9^((1/2)(x-6))

 

[pka]

find the solution of the exponential equation:
3^2x= 9^((1/2)(x-6))

Hint: \(\displaystyle 9^{\frac{x-6}{2}}=3^{x-6}\)

 

[chutch82]

i got x=12.

 

[pka]

i got x=12.

It should be \(\displaystyle x=-6\)

 

[chutch82]

would this equation be kind of the same idea.

find the largest solution of the exponential equation:
2^x^2= 4^(-5/2)(x)+12

 

[pka]

would this equation be kind of the same idea.

find the largest solution of the exponential equation:
2^x^2= 4^(-5/2)(x)+12

Do you mean \(\displaystyle 4^{\frac{-5x}{2}+12}~?\) OR \(\displaystyle 4^{\frac{-5x+12}{2}}~?\)

 

[chutch82]

the first one.

 

[pka]

\(\displaystyle 4^{\frac{-5x}{2}+12}=2^{-5x+24}\)

 

[lookagain]

find the solution of the exponential equation:

3^2x= 9^((1/2)(x-6))

chutch82,

you need grouping symbols, such as parentheses, around "2x" if you mean for it to be \(\displaystyle 3^{2x}. \)


What you have on the left-hand side of the equals sign is the same as (3^2)x, or 9x.


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would this equation be kind of the same idea.

find the largest solution of the exponential equation:
2^x^2= 4^(-5/2)(x)+12

​

2^x^2 is ambiguous.

For instance, on the www.quickmath.com site, 2^3^2 = \(\displaystyle \ 2^{3^2} \ = \ 2^9 \ = \ 512.\)


But on my TI-83 graphics calculator, 2^3^2 is calculated as (2^3)^2 = \(\displaystyle \ 8^2 \ = \ 64.\)

(I would take it that the calculator is treating it as "first come first serve" on
exponentiation done from left to right.)


I suggest you type (2^x)^2 if you mean \(\displaystyle (2^x)^2 \ \ or\)

type 2^(x^2) if you mean \(\displaystyle 2^{x^2}.\)