Question

(0,1)^(2х-3)=10^(х-0,3)

Answer 1

Ответ:

0,1^(2x-3) = 10  

2х - 3 = -1  

2х = 2  

х = 1

Пошаговое объяснение:

Answer 2

To solve the equation, we can start by taking the logarithm of both sides. We can use any base for the logarithm, but let's use the natural logarithm (ln) for simplicity:

ln((0,1)^(2x-3)) = ln(10^(x-0.3))

Using the properties of logarithms, we can rewrite the equation as:

(2x - 3) * ln(0.1) = (x - 0.3) * ln(10)

Now, let's simplify further:

2x * ln(0.1) - 3 * ln(0.1) = x * ln(10) - 0.3 * ln(10)

Next, we can isolate the terms with x on one side of the equation:

2x * ln(0.1) - x * ln(10) = 3 * ln(0.1) - 0.3 * ln(10)

Now, we can factor out x:

x * (2 * ln(0.1) - ln(10)) = 3 * ln(0.1) - 0.3 * ln(10)

Finally, we solve for x by dividing both sides of the equation by the coefficient of x:

x = (3 * ln(0.1) - 0.3 * ln(10)) / (2 * ln(0.1) - ln(10))

Now, you can use a calculator or software to approximate the value of x.