Question

Обчислити (log9 4)^2+(log15 3)^2

Answer 1

Ответ:

=(9 4 ² +(log15 3 *2)= 2*4²*9= 288

Answer 2

To compute the expression (log₉4)² + (log₁₅3)², we need to evaluate the logarithmic expressions first, and then perform the necessary arithmetic operations.

Step 1: Calculate the logarithmic values.

log₉4 represents the logarithm of 4 to the base 9. log₉4 = log(4) / log(9)

log₁₅3 represents the logarithm of 3 to the base 15. log₁₅3 = log(3) / log(15)

Step 2: Evaluate the logarithmic expressions.

Using a calculator or mathematical software, we find:

log₉4 ≈ 0.5 log₁₅3 ≈ 0.292

Step 3: Compute the expression.

(log₉4)² + (log₁₅3)² ≈ (0.5)² + (0.292)² ≈ 0.25 + 0.085264 ≈ 0.335264

So, (log₉4)² + (log₁₅3)² ≈ 0.335264.