Question

∛-125 ⁴√1/16 (дробная) ⁵√-1024⁴√625∛-27/8 (дробная)⁴√⁵√12∛√6log₃ x= -4log₂ x= 3

Answer 1

∛-125=-5
⁴√1/16 =1/2

⁵√-1024=-4
⁴√625=5
∛-27/8 = -3/2

⁴√⁵√12=²⁰√12
∛√6=⁶√6

log₃ x= -4  x=3^(-4)=1/81
log₂ x= 3   x=2^3=8

Answer 2

To solve the given equations and expressions, let's break them down step by step:

1. ∛(-125): The cube root of -125 is -5 since (-5)^3 = -125.

2. ⁴√(1/16): The fourth root of 1/16 is 1/2 since (1/2)^4 = 1/16.

3. ⁵√(-1024): The fifth root of -1024 is -4 since (-4)^5 = -1024.

4. ⁴√625: The fourth root of 625 is 5 since 5^4 = 625.

5. ∛(-27/8): Simplifying the expression -27/8, we have -27/8 = -(3^3)/(2^3) = -27/8 = -3/2. Therefore, the cube root of -27/8 is -3/2.

6. (дробная)⁴√⁵√12: It's not clear what the term "(дробная)" refers to. Please provide more context or clarification.

7. ∛√6: The cube root of the square root of 6 is √(6^(1/2)) = √(√6) = (√6)^(1/2) = 6^(1/4) = √(6^(1/2)) = √(√6) = (√6)^(1/2) = 6^(1/4).

8. log₃x = -4: To solve this equation, we need to apply logarithmic properties. Taking the logarithm base 3 of both sides, we have: log₃x = -4 x = 3^(-4) x = 1/81

9. log₂x = 3: Similar to the previous equation, taking the logarithm base 2 of both sides, we have: log₂x = 3 x = 2^3 x = 8

Please note that the solution to the equation log₃x = -4 may not be valid if the logarithm is only defined for positive values of x.