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Solve ln(5x+7)=8
. Round to the nearest thousandth.
To solve the equation ln(5x + 7) = 8, we first need to isolate x.
1. Start by rewriting the equation using the definition of natural logarithm:
e^8 = 5x + 7
2. Next, subtract 7 from both sides:
e^8 - 7 = 5x
3. Now, divide by 5 to solve for x:
x = (e^8 - 7) / 5
4. Calculate the value of x using a calculator:
x ≈ (e^8 - 7) / 5
x ≈ (2980.96 - 7) / 5
x ≈ 2973.96 / 5
x ≈ 594.792
Therefore, the solution to the equation ln(5x + 7) = 8 rounded to the nearest thousandth is x ≈ 594.792.