Question

Find the domain of the function f(x)=ln(x−6)+ln(x−8)

Answer 1

To find the domain of the function f(x) = ln(x-6) + ln(x-8), we set the expressions inside the logarithm functions to be greater than 0. The domain is x > 8.

Step-by-step explanation:

Domain of the Function

To find the domain of the function f(x) = ln(x-6) + ln(x-8), we need to identify the values of x that make the expression inside the logarithm functions valid. Since the natural logarithm is only defined for positive values, we need to ensure that both x-6 and x-8 are greater than 0.

Step 1:

Set x-6 > 0 and solve for x:

x - 6 > 0

x > 6

Step 2:

Set x-8 > 0 and solve for x:

x - 8 > 0

x > 8

Step 3:

Combine the two intervals where x > 6 and x > 8:

x > 8

The domain of the function f(x) = ln(x-6) + ln(x-8) is x > 8.

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