Question

2^x+2^x+2^x+2^x/4^x+4^x+4^x+4^x=16^1-2x решите уравнение

Answer 1

Если предположить, что вы забыли написать скобки в знаменателе и степени, то решение такое

Answer 2

To solve the equation, let's simplify the left-hand side first:

2^x + 2^x + 2^x + 2^x / 4^x + 4^x + 4^x + 4^x

Since 4^x is equal to (2^2)^x, we can rewrite the expression:

2^x + 2^x + 2^x + 2^x / (2^2)^x + (2^2)^x + (2^2)^x + (2^2)^x

Now, we can use the property of exponents: (a^m)^n = a^(m*n)

2^x + 2^x + 2^x + 2^x / 2^(2x) + 2^(2x) + 2^(2x) + 2^(2x)

Combine like terms:

4 * 2^x / 4 * 2^(2x)

Now, we can cancel out the common terms:

2^x / 2^(2x)

Using the property of exponents: a^m / a^n = a^(m-n)

2^(x - 2x)

Now, the left-hand side of the equation becomes:

2^(x - 2x) = 16^(1 - 2x)

Next, we simplify 16^(1 - 2x):

16 = 2^4, so 16^(1 - 2x) = (2^4)^(1 - 2x)

Using the property of exponents: (a^m)^n = a^(m*n)

16^(1 - 2x) = 2^(4(1 - 2x))

16^(1 - 2x) = 2^(4 - 8x)

Now the equation becomes:

2^(x - 2x) = 2^(4 - 8x)

Now, we have a base of 2 raised to two different exponents that are equal to each other. To find the solution, we can set the exponents equal to each other:

x - 2x = 4 - 8x

Combine like terms:

-x = 4 - 8x

Add 8x to both sides:

8x - x = 4

7x = 4

Divide by 7:

x = 4 / 7

So, the solution to the equation is:

x = 4 / 7