Question

HELP!!! 2^(x-3)=3^(3-x)

Answer 1

Решение:
2^(x-3)=3^(3-x)
2^x/2^3=3^3/3^x
2^x*3^x=2^3*3^3
(2*3)^x=(2*3)^3
6^x=6^3
x=3

Ответ: х=3

Answer 2

To solve the equation 2^(x-3) = 3^(3-x), we can take the logarithm of both sides. Using the natural logarithm (ln) for simplicity, we have:

ln(2^(x-3)) = ln(3^(3-x))

Using the logarithmic property that ln(a^b) = b * ln(a), we can simplify further:

(x-3) * ln(2) = (3-x) * ln(3)

Expand the multiplication:

x * ln(2) - 3 * ln(2) = 3 * ln(3) - x * ln(3)

Move the x terms to one side and the constant terms to the other side:

x * ln(2) + x * ln(3) = 3 * ln(3) + 3 * ln(2)

Factor out x:

x * (ln(2) + ln(3)) = 3 * (ln(3) + ln(2))

Divide both sides by (ln(2) + ln(3)):

x = 3 * (ln(3) + ln(2)) / (ln(2) + ln(3))

Calculating this expression gives you the approximate value of x.