Question

Log¹²144×log²8÷log½81=​

Answer 1

Ответ:

Объяснение:

log(12)(144)= log(12)(12²)= 2

log(2)(8)= log(2)(2³)= 3

log(1/2)(81)= -4log(2)(3)

2*3:(-4log(2)(3))= 6:(-4log(2)(3))= -3/log(2)(9)

Answer 2

To solve the expression, let's break it down step by step:

1. Calculate log¹²144: log₁₂144 = x, which means 12^x = 144. Since 12^2 = 144, we get x = 2.

2. Calculate log²8: log₂8 = y, which means 2^y = 8. Since 2^3 = 8, we get y = 3.

3. Calculate log½81: log½81 = z, which means 1/2^z = 81. To find z, rewrite 81 as a power of 2: 81 = 3^4 = (2^2)^4 = 2^8. So, 1/2^z = 2^8. By taking the reciprocal, 2^z = 2^(-8). For them to be equal, z = -8.

Now, substitute the values of x, y, and z into the original expression:

log¹²144 × log²8 ÷ log½81 = 2 × 3 ÷ (-8) = 6 ÷ (-8) = -3/4.

Therefore, the result of the expression is -3/4.