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Q4 Q23.) Solve the following exponential equation. Express the solution set in terms of natural logarithms. Then use a calculator to obtain a decimal​ approximation, correct to two decimal​ places, for the solution.

Q4 Q23 Solve the following exponential equation Express the solution set in terms of natural logarithms Then use a calculator to obtain a decimal approximation class=

Respuesta :

sqdancefan
Let z = e^(2x). Then your equation is
  z^2 +3z -28 = 0
  (z +7)(x -4) = 0
  z = -7 or 4

Taking the log of our definition of z, we have
  ln(z) = 2x
  x = ln(z)/2
So, the one real solution is
  x = ln(4)/2 = ln(√4)
  x = ln(2)
The decimal approximation is
  x ≈ 0.69
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