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