Solve the logarithmic equation. Use the definition of logarithm or the definition of natural logarithm. (Enter your answers as a comma-separated list.)ln(7x − 5) = 3

To solve the logarithmic equation ln(7x - 5) = 3, follow these steps:

Step 1: Understand that ln is the natural logarithm, which is the logarithm to the base e, where e is approximately equal to 2.71828.

Step 2: To remove the natural logarithm from the equation, you can use the property of logarithms that says if ln(a) = b, then e^b = a. So, we can rewrite the equation as e^3 = 7x - 5.

Step 3: Simplify e^3. e^3 is approximately equal to 20.0855.

Step 4: So, the equation becomes 20.0855 = 7x - 5.

Step 5: Add 5 to both sides of the equation to isolate the term with x. This gives 25.0855 = 7x.

Step 6: Divide both sides of the equation by 7 to solve for x. This gives x = 25.0855 / 7.

Step 7: Simplify 25.0855 / 7 to get the solution for x. x is approximately equal to 3.5836.

So, the solution to the equation ln(7x - 5) = 3 is x ≈ 3.5836.

To solve the logarithmic equation ln(7x - 5) = 3, you can follow these steps:

Step 1: Understand that ln is the natural logarithm, which is the logarithm to the base e, where e is approximately equal to 2.71828.

Step 2: To remove the natural logarithm from the equation, you can use the property of logarithms that says if ln(a) = b, then e^b = a. So, you can rewrite the equation as e^3 = 7x - 5.

Step 3: Simplify e^3. e^3 is approximately equal to 20.0855.

Step 4: So, the equation becomes 20.0855 = 7x - 5.

Step 5: Add 5 to both sides of the equation to isolate the term with x. This gives you 25.0855 = 7x.

Step 6: Divide both sides of the equation by 7 to solve for x. This gives you x = 25.0855 / 7.

Step 7: Simplify the right side to find the value of x. x is approximately equal to 3.5836.

So, the solution to the equation ln(7x - 5) = 3 is x ≈ 3.5836.