Amenah8
  • Amenah8
Calculus: rewrite 9^2x, base 3
Mathematics
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Amenah8
  • Amenah8
Calculus: rewrite 9^2x, base 3
Mathematics
katieb
  • katieb
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phi
  • phi
can you write 9 as 3 to some power?
Amenah8
  • Amenah8
3^2
Amenah8
  • Amenah8
now what do i do?

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Amenah8
  • Amenah8
|dw:1439220479304:dw|
anonymous
  • anonymous
Replace 9 by 3^2...
anonymous
  • anonymous
|dw:1439220587021:dw|
Amenah8
  • Amenah8
3^2(2x), base 3?
Amenah8
  • Amenah8
3^4x?
phi
  • phi
did we start with \[ 9^{2x} \] ?
anonymous
  • anonymous
3^{4x} is good to me..
phi
  • phi
if so then we replace 9 with 3^2 \[ \left(3^2\right)^{2x} \] and use the rule \[ \left(a^b\right)^c = a^{b\cdot c} \] to get \[ 3^{2\cdot 2\cdot x} = 3^{4x} \]
anonymous
  • anonymous
\[(a^m)^n = (a)^{m \times n}\]
Amenah8
  • Amenah8
so sorry something went wrong with my computer. thanks for staying
Amenah8
  • Amenah8
ah! okay i'm back now, sorry
Amenah8
  • Amenah8
so now i have 3^4x, base 3. does the base 3 just mean that, by replacing 9 with 3^2, I got a base of 3? or do i somehow have to apply base 3 to 3^4x?
Vocaloid
  • Vocaloid
yeah, you're done. 3^4x is already in base 3, since 3 is being raised to a power
Amenah8
  • Amenah8
thanks so much!! this is just a quick question, but what would i do for a problem like this where i have to make a fraction 1/8 with a base of 2?
Vocaloid
  • Vocaloid
similar process, except we're dealing with a negative exponent 1/8 = 1/2^3 = 2^(-3)
Amenah8
  • Amenah8
how did you know it was 1/2^3?
Vocaloid
  • Vocaloid
8 = 2^3 therefore 1/8 = 1/2^3
Vocaloid
  • Vocaloid
to make a bit more clear 1/8 = 1/(2^3)
Amenah8
  • Amenah8
i get it! thank you os much!!

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