To solve the equation log2^2(x-1) - 5log2(x-1) - 6 = 0, we can use a substitution to simplify the equation. Let's denote log2(x-1) as y.
Substituting y into the equation, we gety^2 - 5y - 6 = 0
Now, we can factor this quadratic equation(y - 6)(y + 1) = 0
Setting each factor to zero, we gety - 6 = y = 6
any + 1 = y = -1
Now, we can substitute back in the original variablelog2(x-1) = x-1 = 2^x-1 = 6x = 65
anlog2(x-1) = -x-1 = 2^-x-1 = 1/x = 1/2 + x = 3/2
Therefore, the solutions to the equation log2^2(x-1) - 5log2(x-1) - 6 = 0 are x = 65 and x = 3/2.
To solve the equation log2^2(x-1) - 5log2(x-1) - 6 = 0, we can use a substitution to simplify the equation. Let's denote log2(x-1) as y.
Substituting y into the equation, we get
y^2 - 5y - 6 = 0
Now, we can factor this quadratic equation
(y - 6)(y + 1) = 0
Setting each factor to zero, we get
y - 6 =
y = 6
an
y + 1 =
y = -1
Now, we can substitute back in the original variable
log2(x-1) =
x-1 = 2^
x-1 = 6
x = 65
an
log2(x-1) = -
x-1 = 2^-
x-1 = 1/
x = 1/2 +
x = 3/2
Therefore, the solutions to the equation log2^2(x-1) - 5log2(x-1) - 6 = 0 are x = 65 and x = 3/2.