Finite Math Examples

Find the Domain log base 5 of 3x^(1/2)
Step 1
Convert expressions with fractional exponents to radicals.
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Step 1.1
Apply the rule to rewrite the exponentiation as a radical.
Step 1.2
Anything raised to is the base itself.
Step 2
Set the argument in greater than to find where the expression is defined.
Step 3
Solve for .
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Step 3.1
To remove the radical on the left side of the inequality, square both sides of the inequality.
Step 3.2
Simplify each side of the inequality.
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Step 3.2.1
Use to rewrite as .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Simplify .
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Step 3.2.2.1.1
Apply the product rule to .
Step 3.2.2.1.2
Raise to the power of .
Step 3.2.2.1.3
Multiply the exponents in .
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Step 3.2.2.1.3.1
Apply the power rule and multiply exponents, .
Step 3.2.2.1.3.2
Cancel the common factor of .
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Step 3.2.2.1.3.2.1
Cancel the common factor.
Step 3.2.2.1.3.2.2
Rewrite the expression.
Step 3.2.2.1.4
Simplify.
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
Raising to any positive power yields .
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Cancel the common factor of .
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Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Divide by .
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Divide by .
Step 3.4
Find the domain of .
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Step 3.4.1
Set the radicand in greater than or equal to to find where the expression is defined.
Step 3.4.2
The domain is all values of that make the expression defined.
Step 3.5
The solution consists of all of the true intervals.
Step 4
Set the radicand in greater than or equal to to find where the expression is defined.
Step 5
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 6