Question

2x-lg(5^2x +x -2)=lg4^x

Answer 1

Пошаговое объяснение:

см фото,,,,,,,,,,,,,,,,,,,,,,

Answer 2

To solve the equation:

2x - lg(5^(2x + x - 2)) = lg(4^x)

First, let's simplify the equation by using the properties of logarithms:

2x - lg(5^(3x - 2)) = lg(2^(2x))

Now, we'll use the property of logarithms that allows us to bring the exponent down in front:

2x - (3x - 2) * lg(5) = 2x * lg(2)

Next, distribute the lg(5) on the left side:

2x - 3x * lg(5) + 2 * lg(5) = 2x * lg(2)

Now, let's isolate the terms with x on one side of the equation and the constant terms on the other side:

2x - 3x * lg(5) - 2x * lg(2) = -2 * lg(5)

Now, we can combine the x terms:

2x - 3x * lg(5) - 2x * lg(2) = -2 * lg(5)

-3x * lg(5) - 2x * lg(2) = -2 * lg(5)

Now, factor out the common term of x:

x(-3 * lg(5) - 2 * lg(2)) = -2 * lg(5)

To solve for x, divide both sides by the coefficient of x:

x = (-2 * lg(5)) / (-3 * lg(5) - 2 * lg(2))

Now, you can calculate the value of x using logarithmic properties:

x = (2 * lg(5)) / (3 * lg(5) + 2 * lg(2))

x ≈ 0.616 (rounded to three decimal places)