Question

3) 81 log9 2 – 0,25log3 2​

Answer 1

Ответ:

Объяснение:

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Answer 2

To simplify the expression 81 log9 2 - 0.25 log3 2, we can start by using the logarithmic property that states:

loga b^n = n * loga b

Let's simplify each term separately:

1. 81 log9 2: We can rewrite 81 as 9^2. Applying the logarithmic property, we have: log9 2 = log(2) / log(9) Since log(2) and log(9) have the same base (commonly base 10), we can divide the logarithms: log9 2 = log(2) / log(9) = log(2) / log(3^2) = log(2) / (2 * log(3))

   Therefore, 81 log9 2 becomes: 9^2 * (log(2) / (2 * log(3))) = 81 * (log(2) / (2 * log(3))) = 81log2/2log3 = 40.5log2/log3

2. -0.25 log3 2: We can directly multiply -0.25 by log3 2: -0.25 * log3 2 = -0.25log3 2

Combining the simplified terms, the expression 81 log9 2 - 0.25 log3 2 can be written as: 40.5 log2 / log3 - 0.25 log3 2