Question

Найдите область определения функции (по теме логарифм):

Answer 1

(x-1)/(x+5)>0   x≠-5   второе условие влечет выполнение этого.
log3 (x-1)/(x+5)≥0=log3(1)   (x-1)/(x+5)≥1   (x-1)/(x+5)-1≥0
[x-1-x-5]/(x+5)≥0   -6/(x+5)≥0   x+5≤0  x≤5 но х≠5 → х<5
ответ  x<5

Answer 2

Finding the Domain of a Logarithmic Function

The domain of a logarithmic function is the set of all real numbers that can be input into the function. For the function \( f(x) = \log_a(bx) \), where \( a \) is the base and \( bx \) is the argument, the domain is determined by the restrictions on the argument of the logarithm.

Key Points: - The argument of a logarithm must be greater than 0. - The domain of a logarithmic function is the set of all real numbers that satisfy this condition.

Now, let's find the domain of the given function \( f(x) = \log_2(7x-x) \).

The argument of the logarithm in this function is \( 7x-x \). To find the domain, we need to determine the values of \( x \) that make the argument greater than 0.

Calculating the Domain

To find the domain, we solve the inequality \( 7x-x > 0 \).

Solution: \[ 7x - x > 0 \] \[ 6x > 0 \] \[ x > 0 \]

So, the domain of the function \( f(x) = \log_2(7x-x) \) is all real numbers \( x \) such that \( x > 0 \).

This means that the function is defined for all real numbers greater than 0.

Summary: - The domain of the function \( f(x) = \log_2(7x-x) \) is \( x > 0 \).

I hope this helps! If you have any further questions, feel free to ask.