To solve this problem, we can use the properties of logarithms to combine the two logarithmic terms into one.
First, let's rewrite the equation using the properties of logarithms:
log1/2(x^2) - log1/2(x) = 6
Next, we can use the property of logarithms that states: log_b(x) - log_b(y) = log_b(x/y)
Therefore, we can rewrite the equation as:
log1/2(x^2 / x) = 6
Simplify the expression inside the logarithm:
log1/2(x) = 6
Now, since the base of the logarithm is 1/2, we can rewrite the equation in exponential form:
1/2^6 = x
x = 1/64
So, the solution to the equation log1/2(x^2) - log1/2(x) = 6 is x = 1/64.
To solve this problem, we can use the properties of logarithms to combine the two logarithmic terms into one.
First, let's rewrite the equation using the properties of logarithms:
log1/2(x^2) - log1/2(x) = 6
Next, we can use the property of logarithms that states: log_b(x) - log_b(y) = log_b(x/y)
Therefore, we can rewrite the equation as:
log1/2(x^2 / x) = 6
Simplify the expression inside the logarithm:
log1/2(x) = 6
Now, since the base of the logarithm is 1/2, we can rewrite the equation in exponential form:
1/2^6 = x
x = 1/64
So, the solution to the equation log1/2(x^2) - log1/2(x) = 6 is x = 1/64.