Solve the Equation

Solve the following equation. Write the answer in terms of the natural logarithm.

Question

Solve the Equation

Solve the following equation. Write the answer in terms of the natural logarithm.

BlackTom AI · Accepted Answer

The equation to solve is e^(2x) = 9. 
Option 1: ln(9)/2. This comes from applying the natural logarithm to both sides: 2x = ln(9), hence x = ln(9)/2. This is a correct expression for the solution.
Option 2: ln(3). Since 9 = 3^2, we have ln(9) = ln(3^2) = 2 ln(3). Therefore ln(9)/2 = (2 ln(3))/2 = ln(3). Thus x = ln(3) is also a correct expression for the same solution.
In summary, both forms ln(9)/2 and ln(3) are equivalent representations of the solution to e^(2x) = 9, so either can be considered correct depending on how the answer is presented.

MAT-265-OD24-02-7799

Solve the Equation Solve the following equation. Write the answer in terms of the natural logarithm.

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