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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.
First, we need to exponentiate both sides using e, the base of natural logarithms:
e^(ln(5x+7)) = e^8
5x+7 = e^8
Next, we need to isolate x by subtracting 7 from both sides:
5x = e^8 - 7
Finally, divide by 5 to solve for x:
x = (e^8 - 7) / 5
Using a calculator to evaluate this expression gives:
x ≈ (2980.96 - 7) / 5
x ≈ 295.992
Therefore, the solution to ln(5x+7) = 8 is x ≈ 295.992. Rounded to the nearest thousandth, x ≈ 296.