0,5log4(x-2)+log16(x-3)=0,25.

Предыдущий
вопрос Следующий
вопрос

First, we need to combine the logarithms using the properties of logarithms.

0,5log4(x-2) + log16(x-3) = 0,25
log4(sqrt(x-2)) + log16(x-3) = 0,25

Next, we can combine the logarithms into a single logarithm using the property loga(x) + loga(y) = loga(xy).

log4(sqrt(x-2)) + log16(x-3) = 0,25
log4(sqrt(x-2)*(x-3)) = 0,25

Now, we can solve for x:

4^(0,25) = sqrt(x-2)(x-3)
2 = sqrt(x-2)(x-3)
4 = (x-2)*(x-3)
4 = x^2 - 5x + 6
0 = x^2 - 5x + 2

Now we can use the quadratic formula to solve for x:

x = [5 ± sqrt(5^2 - 412)] / 2
x = [5 ± sqrt(25 - 8)] / 2
x = [5 ± sqrt(17)] / 2

Therefore, the solutions for x are:

x = (5 + sqrt(17)) / 2 and x = (5 - sqrt(17)) / 2.