Solve ln (5x + 1) = 3.
Round to the nearest thousandth.
We can solve for x by first applying the exponential function e to both sides of the equation to get rid of the natural logarithm. This gives:
e^(ln(5x + 1)) = e^3.
Since e^(ln(x)) = x for any positive x, we can simplify the equation to:
5x + 1 = e^3.
Next, we can subtract 1 from both sides:
5x = e^3 - 1.
Finally, we can divide both sides by 5 to solve for x:
x = (e^3 - 1) / 5.
Using a calculator, we find:
x ≈ 3.195.
Therefore, rounded to the nearest thousandth, the solution is x ≈ 3.195.
are you sure
I apologize for any confusion in my previous response. Let's solve the equation step by step to ensure accuracy.
To start, we have the equation ln(5x + 1) = 3.
First, we can rewrite the equation using the property of logarithms that ln(e^a) = a:
5x + 1 = e^3.
Next, we subtract 1 from both sides:
5x = e^3 - 1.
Finally, we divide both sides by 5:
x = (e^3 - 1) / 5.
Now, let's calculate the value using a calculator to three decimal places:
x ≈ (e^3 - 1) / 5 ≈ (20.085 - 1) / 5 ≈ 19.085 / 5 ≈ 3.817.
Rounding to the nearest thousandth, the solution is x ≈ 3.817.
I apologize again for any confusion caused earlier and hope this clears it up.