What is the domain of y= log3 ( 5x^2-125) ?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The log function is defined for all numbers greater than 0.

The domain of a function f(x) is all values of x for which f(x) is defined.

For y = log(3) (5x^2 - 125) we should have 5x^2 - 125 > 5 for y to be defined.

5x^2 - 125 > 0

=> x^2 > 125/5

=> x^2 > 25

=> x > 5 and x < -5

The domain of the function is (-inf , -5) U (5 , inf.)

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

y= log3 ( 5x^2-125)

We need to find the domain.

The domain is all x values such that the function y is defined.

Since the function is a logarithm, then we know that the logarithm should be greater than, zero.

==> (5x^2-125) > 0

We will add 125 to both sides.

==> 5x^2 > 125

==> x^2 > 25

==> l x l > 5

==> x > 5  and x < -5

Then the domain is :

x = ( -inf, -5) U (5, inf)

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The domain of f(x) = `log_3 ( 5x^2-125)` has to be determined. The domain of a function f(x) is the set of values in which x lies such that the value of f(x) is real and defined.

The logarithm of 0 or a negative number is not defined.

As a result 5x^2 - 125 > 0

x^2 > 25

=> -5 < x and x > 5

The required domain is `(-oo, -5)U(5, oo)`

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