Question

The domain of y=log3(x+5) in the real numbers

Answer 1

ANSWER

The domain is
$x > - 5$
or

$(-5, \infty )$


EXPLANATION

The domain refers to all values of x for which the logarithmic function
$y = log3(x + 5)$
is defined.

The logarithmic function is defined for all positive real numbers.


To determine the domain, we need to restrict the argument of this function to be greater than zero.


Thus,

$3(x + 5) > \: 0$


We now solve for x by dividing through by 3 to obtain,

$x + 5 \: > \: 0$

This implies that,

$x \: > \: 0$