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Solve ln(5x+7)=8
. Round to the nearest thousandth.
To solve the equation ln(5x+7)=8, we need to isolate x.
First, we can exponentiate both sides of the equation using the fact that e^ln(y) = y:
e^(ln(5x+7)) = e^8
This simplifies to:
5x + 7 = e^8
Next, we can subtract 7 from both sides:
5x = e^8 - 7
Finally, we can divide both sides by 5 to solve for x:
x = (e^8 - 7) / 5
Rounding to the nearest thousandth:
x ≈ (2980.96 - 7) / 5
x ≈ 2973.96 / 5
x ≈ 594.792