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3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0 .
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3 ^ (2x) - 2 ^ (x + 1) * 3 ^ x - 3 * 2 ^ (2x) = 0 .

User Thousight
by
7.1k points

1 Answer

2 votes

Answer:

log₁.₅3 or 2.70951

Explanation:

  • 3^(2x) - 2^(x + 1) * 3^x - 3*2^(2x) = 0
  • 3^(2x)- 2*2^x*3^x + 2^(2x)- 4*2^(2x)=0
  • (3^x-2^x)^2 - (2*2^x)^2=0
  • (3^x-2^x+2*2^x)(3^x - 2^x - 2*2^x)=0
  • (3^x+2^x)(3^x- 3*2^x)=0
  • 3^x+2^x>0 for any value of x
  • 3^x- 3*2^x=0
  • 3^x= 3*2^x
  • 3^x/2^x=3
  • 1.5^x=3
  • x= log₁.₅ 3 = 2.70951

User Attila Fulop
by
7.1k points
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