Question

Log 0,5 ^2x-log 0,5^x-2=0

Answer 1

Ответ:

некорректно написано уравнение

Answer 2

To solve the equation log(0.5)^(2x) - log(0.5)^x - 2 = 0, let's simplify it step by step:

First, we can rewrite the equation using the properties of logarithms:

2x * log(0.5) - x * log(0.5) - 2 = 0

Next, notice that both terms have a common factor of log(0.5). We can factor it out:

log(0.5) * (2x - x) - 2 = 0

Simplifying further:

log(0.5) * x - 2 = 0

Now, let's isolate x by moving the constant term to the other side:

log(0.5) * x = 2

To solve for x, we can exponentiate both sides with base 0.5. Remember that the logarithmic equation log(base b)(a) = c is equivalent to b^c = a.

0.5^(log(0.5) * x) = 0.5^2

0.5^x = 0.25

Now, we have a simpler equation. Taking the logarithm of both sides, we can solve for x:

log(0.5^x) = log(0.25)

x * log(0.5) = log(0.25)

Using the properties of logarithms, we can simplify the right side further:

x * log(0.5) = log(0.5^2)

x * log(0.5) = log(0.25)

Now, dividing both sides by log(0.5):

x = log(0.25) / log(0.5)

Using logarithmic properties again, we can simplify:

x = log(0.25) / log(0.5)

x = log(0.5^-2) / log(0.5)

Applying the property log(base b)(a^c) = c * log(base b)(a):

x = -2 * log(0.5) / log(0.5)

Finally, calculating the values:

x = -2 * (-1) / (-0.3010)

x = 2 / 0.3010

x ≈ 6.644

Therefore, the solution to the equation log(0.5)^(2x) - log(0.5)^x - 2 = 0 is approximately x = 6.644.