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Use natural logarithms to solve the equation. Round to the nearest thousandth.
5e2x+11=30
To solve the equation 5e^(2x) + 11 = 30 using natural logarithms, we need to isolate the exponential term first.
Step 1: Subtract 11 from both sides of the equation
5e^(2x) = 19
Step 2: Divide both sides by 5
e^(2x) = 3.8
Step 3: Take the natural logarithm of both sides
ln(e^(2x)) = ln(3.8)
2x = ln(3.8)
Step 4: Divide by 2
x = ln(3.8) / 2 ≈ 0.639
Therefore, the solution to the equation is x ≈ 0.639.