Answer:
Explanation:
To solve the equation e^(4x-1) = 3, we can take the natural logarithm (ln) of both sides of the equation.
Applying the natural logarithm to both sides gives us:
ln(e^(4x-1)) = ln(3).
Using the property of logarithms that states ln(a^b) = b * ln(a), we can simplify the left side of the equation:
(4x-1) * ln(e) = ln(3).
Since ln(e) equals 1, the equation becomes:
4x - 1 = ln(3).
To isolate x, we add 1 to both sides:
4x = 1 + ln(3).
Finally, we divide both sides by 4 to solve for x:
x = (1 + ln(3))/4.
Therefore, the exact solution to the equation e^(4x-1) = 3 is x = (1 + ln(3))/4.