Question

Решить уравнение: log6(x-5)=2

Answer 1

Ответ:

Пошаговое объяснение:

x-5>0   x>5

6^2=x-5

x=41

Answer 2

Ответ:

x–5=62

x–5=36

x=41

Пошаговое объяснение:

Answer 3

To solve the equation log₆(x - 5) = 2, you can follow these steps:

Step 1: Rewrite the equation in exponential form using the definition of a logarithm. The logarithm function logₐ(b) = c is equivalent to saying a^c = b.

So, log₆(x - 5) = 2 can be rewritten as 6^2 = x - 5.

Step 2: Simplify the exponential equation:

6^2 = 36.

So, the equation now becomes:

36 = x - 5.

Step 3: Solve for x:

Add 5 to both sides of the equation:

36 + 5 = x, 41 = x.

Step 4: Check the solution:

Now, we need to check if x = 41 is a valid solution for the original equation:

log₆(41 - 5) = log₆(36) = 2.

Since the left-hand side equals the right-hand side (2 = 2), the solution x = 41 is valid.

Therefore, the solution to the equation log₆(x - 5) = 2 is x = 41.