Question

Найти значение логоритфмов1) log 7 492)log 1/2 1/163) log 5 14) log 0.2 125

Answer 1

1) 2

2) 4

3) 0

4) -3

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Answer 2

To find the values of the given logarithms, we can use the following properties of logarithms:

1. log_a(b) = c if and only if a^c = b.

Now, let's calculate the values:

1. log base 7 of 49 Here, we want to find c in the equation 7^c = 49. Since 7^2 = 49, we have log base 7 of 49 = 2.

2. log base 1/2 of 1/16 Here, we want to find c in the equation (1/2)^c = 1/16. Since (1/2)^4 = 1/16, we have log base 1/2 of 1/16 = 4.

3. log base 5 of 1 Here, we want to find c in the equation 5^c = 1. Any nonzero number raised to the power of 0 is equal to 1, so we have log base 5 of 1 = 0.

4. log base 0.2 of 125 Here, we want to find c in the equation 0.2^c = 125. However, it's not possible to raise 0.2 to any power and get 125 as the result. Thus, log base 0.2 of 125 is undefined.

So, the values of the logarithms are:

1. log base 7 of 49 = 2
2. log base 1/2 of 1/16 = 4
3. log base 5 of 1 = 0
4. log base 0.2 of 125 = undefined.