Question

Знайти область визначення функции: f(x)= lg(3x-5)

Answer 1

3x-5>0; x>5/3
D(f)=(5/3; +нескін)

Answer 2

3х-5больше 0; х больше 5/3
D(f) равно (5/3);плюс нескiн

Answer 3

To find the domain of the function $f(x) = \log(3x-5)$, we need to consider the values of $x$ for which the function is defined. The logarithmic function $\log(x)$ is defined only for positive values of $x$. Therefore, for the given function $f(x) = \log(3x-5)$ to be defined, the expression $3x-5$ inside the logarithm must be greater than zero.

We set the expression $3x-5$ greater than zero and solve for $x$:

$3x-5 > 0$

Now, isolate $x$ on one side:

$3x > 5$

$x > \frac{5}{3}$

The domain of the function is all real numbers $x$ greater than $\frac{5}{3}$. In interval notation, the domain can be written as:

$x \in \left(\frac{5}{3}, +\infty\right)$