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Solve the equation for π‘₯π‘₯: 2x+17=3xβˆ’22^x + 17 = 3^x - 2

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Full solution

Q. Solve the equation for π‘₯π‘₯: 2x+17=3xβˆ’22^x + 17 = 3^x - 2
  1. Isolate x terms: First, let's try to isolate the terms with xx on one side of the equation.2x+17=3xβˆ’22^x + 17 = 3^x - 2
  2. Subtract and isolate: Subtract 2x2^x from both sides to get all the xx terms on one side.\newline17=3xβˆ’2xβˆ’217 = 3^x - 2^x - 2
  3. Add to isolate x: Now, add 22 to both sides to isolate the xx terms.\newline19=3xβˆ’2x19 = 3^x - 2^x
  4. Complex algebraic equation: This equation doesn't have a straightforward algebraic solution. We might need to use logarithms or numerical methods to solve it.
  5. Take natural logarithm: Let's try taking the natural logarithm of both sides to see if that helps.\newlineln⁑(19)=ln⁑(3xβˆ’2x)\ln(19) = \ln(3^x - 2^x)

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