use natural logarithms to solve the equation. round to the nearest thousandth.
5e^(2x+11)=30
To solve the equation 5e^(2x+11) = 30 using natural logarithms, you need to isolate the exponential term and take the natural logarithm of both sides.
Divide both sides of the equation by 5:
e^(2x+11) = 30/5
Simplify the right side:
e^(2x+11) = 6
Now, take the natural logarithm of both sides:
ln(e^(2x+11)) = ln(6)
Using the logarithmic property ln(e^a) = a:
2x+11 = ln(6)
Now, isolate the variable x:
2x = ln(6) - 11
Divide both sides of the equation by 2:
x = (ln(6) - 11)/2
Using a calculator or computer software, you can calculate the value of x:
x ≈ -2.042
Rounding to the nearest thousandth, x ≈ -2.042.