Final answer:
To solve the equation 2ln(3) = ln(x - 4), you can first simplify the left side of the equation. Then, equate the exponents of ln(3) on both sides and isolate x. The solution to the equation is x = 13.
Step-by-step explanation:
To solve the equation 2ln(3) = ln(x - 4), we can first simplify the left side of the equation by using the property ln(a) + ln(b) = ln(a * b). This gives us ln(3^2) = ln(x - 4). Next, we can use the fact that ln(a^b) = b * ln(a) to simplify further, resulting in 2 * ln(3) = ln(x - 4). Now, we can equate the exponents of ln(3) on both sides of the equation, and solve for x by isolating it.
2 * ln(3) = ln(x - 4)
ln(3^2) = ln(x - 4)
2 * ln(3) = ln(x - 4)
2 * ln(3) = ln(x - 4)
ln(3) = (1/2) * ln(x - 4)
To isolate x, we can raise both sides of the equation to the power of e (the inverse function of ln):
e^(ln(3)) = e^((1/2) * ln(x - 4))
3 = (x - 4)^(1/2)
Squaring both sides of the equation, we get:
9 = x - 4
Finally, adding 4 to both sides of the equation, we find that:
x = 13