If 3x+1 = 9x-2, find the value of 21+x

Question:

If $3^{x+1}=9^{x-2}$, find the value of $2^{1+x}$

 

Solution:

$3^{x+1}=9^{x-2}$

$3^{x+1}=3^{2 x-4}$

x + 1 = 2x - 4

x = 5

Therefore the value of $2^{1+x}=2^{1+5}=2^{6}=64$

 

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