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Solve ln(5x+7)=8
. Round to the nearest thousandth.
(2 points)
To solve the equation ln(5x+7)=8, we need to isolate the variable x.
Step 1: Take the exponential of both sides with the base e, which is the inverse of the natural logarithm function.
e^(ln(5x+7)) = e^8
Step 2: Simplify the left side of the equation using the logarithmic property log(base a)(a) = 1.
5x+7 = e^8
Step 3: Subtract 7 from both sides to isolate the term with x.
5x = e^8 - 7
Step 4: Divide both sides by 5 to solve for x.
x = (e^8 - 7) / 5
Using a calculator, we can evaluate the right side of the equation:
x ≈ (e^8 - 7) / 5 ≈ (2980.957987 + 1.10364) / 5 ≈ 596.6125258 / 5 ≈ 119.322505
Rounding to the nearest thousandth, the solution to the equation ln(5x+7)=8 is x ≈ 119.323.