Question

5log2(2)-log2(8)+2log2(5)

Answer 1

Ответ:

Пошаговое объяснение:

Если 2 это основание логарифмов, то

5log2(2)-log2(8)+2log2(5)=

5-3+log2(5²)=2+2log2(5)

Answer 2

To simplify the expression, we'll use the logarithmic property:

1. log_b(x^a) = a * log_b(x)

Now, let's simplify the expression step by step:

1. 5log2(2) - log2(8) + 2log2(5)

2. Since log2(2) = 1, we can simplify 5log2(2) to 5 * 1 = 5:

   5 - log2(8) + 2log2(5)

3. Now, let's simplify log2(8). We can rewrite 8 as 2^3:

   5 - log2(2^3) + 2log2(5)

4. By using the logarithmic property mentioned earlier, we can bring down the exponent:

   5 - 3log2(2) + 2log2(5)

5. Again, since log2(2) = 1, we can simplify 3log2(2) to 3 * 1 = 3:

   5 - 3 + 2log2(5)

6. Now, we need to compute log2(5):

   5 - 3 + 2 * log2(5)

   The value of log2(5) is approximately 2.3219.

7. Finally, compute the result:

   5 - 3 + 2 * 2.3219 ≈ 5 - 3 + 4.6438 ≈ 6.6438

So, the simplified expression is approximately 6.6438.