8=4^1/10x+1 (4 в степени 1/10x+1)

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вопрос

To simplify the expression given, we need to rewrite it using the properties of exponents.

We have: 8 = 4^(1/10x+1)

Since 8 is equal to 2^3, we can rewrite the expression as:

2^3 = 4^(1/10x+1)

Since 4 is equal to 2^2, we can rewrite the expression once again as:

2^3 = (2^2)^(1/10x+1)

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

2^3 = 2^(2*(1/10x+1))

Now, multiply 2 by 1/10x and 2 by 1:

2^3 = 2^(2/10x+2)

In order to simplify further, we can rewrite 2 as 2^1:

2^(3) = 2^(2/10x+2)

Since both sides have the same base (2), we can equate the exponents:

3 = 2/10x + 2

Subtract 2 from both sides:

1 = 2/10x

Multiply both sides by 10x:

10x = 2

Divide by 10:

x = 2/10

Therefore, the solution to the equation 8 = 4^(1/10x+1) is x = 1/5.