Question

〖log〗_10 250- 〖log〗_10 2, 5+ 〖log〗_16 〖log〗_6 36

Answer 1

$></p> <p>Ответ: 2.25</p> </div> <div class=$ 0 0

Answer 2

Let's break down the expression step by step:

1. 〖log〗_10 250 - 〖log〗_10 2: To simplify this part, we can use the property of logarithms that states 〖log〗_a (b) - 〖log〗_a (c) = 〖log〗_a (b/c).

So, 〖log〗_10 250 - 〖log〗_10 2 = 〖log〗_10 (250/2) = 〖log〗_10 125.

Now, 125 is equal to 5^3, so 〖log〗_10 125 = 〖log〗_10 (5^3) = 3 〖log〗_10 5.

2. 5 + 〖log〗_16 〖log〗_6 36: First, let's find 〖log〗_6 36. The logarithm base 6 of 36 means "What power do we need to raise 6 to in order to get 36?"

6^2 = 36, so 〖log〗_6 36 = 2.

Now, we need to find 〖log〗_16 2. The logarithm base 16 of 2 means "What power do we need to raise 16 to in order to get 2?"

2 is not a power of 16, but we can express 2 as a power of 16: 2 = 16^(1/4).

So, 〖log〗_16 2 = 1/4.

Now, add the two logarithms together:

5 + 〖log〗_16 〖log〗_6 36 = 5 + 2 + 1/4 = 7 + 1/4 = 7.25.

Putting it all together, the expression becomes:

3 〖log〗_10 5 + 7.25.