Question

Решить уравнение: log 2 ( x - 5) = 3

Answer 1

$log_{2}(x - 5) = 3 \\ x - 5 = {2}^{3} \\ x - 5 = 8 \\ x = 13$
Ответ: 13

Answer 2

To solve the equation log2(x - 5) = 3, we need to use the properties of logarithms. The logarithm equation can be rewritten in exponential form as follows:

loga(b) = c is equivalent to a^c = b.

Using this property, we get:

2^3 = x - 5.

Now, solve for x:

2^3 = 8.

x - 5 = 8.

Add 5 to both sides of the equation:

x = 8 + 5.

x = 13.

Therefore, the solution to the equation is x = 13. You can verify this solution by substituting x with 13 in the original equation to ensure it holds true.