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Use natural logarithms to solve the equation. Round to the nearest thousandth.
5e^2x + 11 = 30
To solve the equation 5e^(2x) + 11 = 30, first subtract 11 from both sides:
5e^(2x) = 19
Next, divide both sides by 5:
e^(2x) = 19/5
Now, take the natural logarithm (ln) of both sides:
ln(e^(2x)) = ln(19/5)
By the logarithmic property, the ln and e^( ) cancels each other out:
2x = ln(19/5)
Finally, divide both sides by 2 to solve for x:
x = ln(19/5)/2
Using a calculator, we find:
x ≈ 0.509.
Therefore, the solution to the equation 5e^(2x) + 11 = 30 is x ≈ 0.509.