solve In(5x+7)=8 round to the nearest thousandth

To solve the equation, we will first isolate the natural logarithm term:

In(5x+7) = 8

Next, we use the property of logarithms that tells us that if ln(b) = a, then b = e^a.
So, we can rewrite the equation as:
5x + 7 = e^8

Subtracting 7 from both sides:
5x = e^8 - 7

Dividing by 5:
x = (e^8 - 7) / 5

Using a calculator, we find that e^8 is approximately equal to 2980.957.

Substituting this value back into the equation, we have:
x ≈ (2980.957 - 7) / 5

Evaluating this expression:
x ≈ 2973.957 / 5

Dividing:
x ≈ 594.791

Rounding this number to the nearest thousandth gives:
x ≈ 594.791