Solve the equation. Check your answer.
ln(5x+2) = 5
To solve the equation ln(5x+2) = 5, we first need to isolate the logarithm term. To do this, we exponentiate both sides of the equation using the natural logarithm base, which is e.
e^ln(5x+2) = e^5
By the property of logarithms that ln(e^x) = x, the left side simplifies to:
5x + 2 = e^5
Next, we subtract 2 from both sides:
5x = e^5 - 2
Finally, we divide both sides by 5 to solve for x:
x = (e^5 - 2)/5
To check our answer, we substitute this value back into the original equation:
ln(5((e^5 - 2)/5) + 2) = 5
Simplifying the expression inside the logarithm:
ln(e^5 - 2 + 2) = 5
ln(e^5) = 5
By the property of logarithms that ln(e^x) = x, the equation becomes:
5 = 5
The left side is equal to the right side, so the solution x = (e^5 - 2)/5 is correct.