anonymous
  • anonymous
Given that 2^(2x+3) x 7^x-2 = 2^3x (49^x), evaluate 14^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ganeshie8
  • ganeshie8
start wid dividing the whole equation wid \(2^{2x+3} 7^{x-2}\)
anonymous
  • anonymous
done it
ganeshie8
  • ganeshie8
\(\large 2^{2x+3} 7^{x-2} = 2^{3x} (49^x)\) \(\large 1 = \frac{2^{3x} (49^x)}{2^{2x+3} 7^{x-2}}\)

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ganeshie8
  • ganeshie8
use exponent properties, and get rid of denominator in right hand side
ganeshie8
  • ganeshie8
also see that you can write 49 as 7^2
anonymous
  • anonymous
seen it i'm ready to move on
ganeshie8
  • ganeshie8
\(\large 2^{2x+3} 7^{x-2} = 2^{3x} (49^x)\) \(\large 1 = \frac{2^{3x} (49^x)}{2^{2x+3} 7^{x-2}}\) \(\large 1 = \frac{2^{3x} (7^{2x})}{2^{2x+3} 7^{x-2}}\) \(\large 1 = \frac{2^{x} (7^{x}) 7^2}{2^{3} }\) \(\large 1 = \frac{14^{x} 7^2}{2^{3} }\)
anonymous
  • anonymous
Thanks for teaching me...
ganeshie8
  • ganeshie8
np :)

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