Question

8^(-1) * 2^3x = 8 Решите пж

Answer 1

2^(-3)*2^3x=2^3

2^3x-3=2^3

3x-3=3

3x=3+3

3x=6

X=2

Answer 2

2^(-3)*2^3x=2^3
2^3x-3=2^3
3x-3=3
3x=3+3
3x=6
X=2

Answer 3

To solve the equation 8^(-1) * 2^3x = 8, we can follow these steps:

Step 1: Simplify the exponents on both sides of the equation. - The exponent -1 means the reciprocal of the base. So, 8^(-1) is equal to 1/8. - The exponent 3x means raising 2 to the power of 3x.

Step 2: Rewrite the equation with the simplified exponents. - The equation becomes (1/8) * 2^(3x) = 8.

Step 3: Simplify the equation further. - We can rewrite 8 as 2^3, since 2^3 is equal to 8. - The equation now becomes (1/8) * 2^(3x) = 2^3.

Step 4: Apply the properties of exponents. - When multiplying two numbers with the same base, we can add their exponents. So, (1/8) * 2^(3x) can be written as 2^(-3) * 2^(3x). - Using the property of exponents, we can add the exponents: 2^(-3) * 2^(3x) = 2^(-3 + 3x).

Step 5: Set the exponents equal to each other. - We have 2^(-3 + 3x) = 2^3.

Step 6: Since the bases are the same, the exponents must be equal. - Therefore, -3 + 3x = 3.

Step 7: Solve for x. - Add 3 to both sides of the equation: -3 + 3 + 3x = 3 + 3. - Simplify: 3x = 6. - Divide both sides by 3: (3x)/3 = 6/3. - Simplify: x = 2.

Therefore, the solution to the equation 8^(-1) * 2^3x = 8 is x = 2.