H(x)=lnx+ln(2-x) find the domain
To find the domain of the function H(x) = ln(x) + ln(2-x), we need to determine the values of x for which the natural logarithm function is defined.
The natural logarithm function ln(x) is defined only for positive real numbers. Therefore, for the first term ln(x) to be defined, x must be greater than zero.
Similarly, for the second term ln(2-x) to be defined, the expression inside the logarithm (2-x) must be greater than zero, which means that x must be less than 2.
Putting both conditions together, the domain of the function H(x) = ln(x) + ln(2-x) is x > 0 and x < 2. In interval notation, the domain is (0, 2).