Precalculus Examples

Evaluate log base 3 of 1/( square root of 3)
Step 1
Multiply by .
Step 2
Combine and simplify the denominator.
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Step 2.1
Multiply by .
Step 2.2
Raise to the power of .
Step 2.3
Raise to the power of .
Step 2.4
Use the power rule to combine exponents.
Step 2.5
Add and .
Step 2.6
Rewrite as .
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Step 2.6.1
Use to rewrite as .
Step 2.6.2
Apply the power rule and multiply exponents, .
Step 2.6.3
Combine and .
Step 2.6.4
Cancel the common factor of .
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Step 2.6.4.1
Cancel the common factor.
Step 2.6.4.2
Rewrite the expression.
Step 2.6.5
Evaluate the exponent.
Step 3
Rewrite as .
Step 4
Rewrite as .
Step 5
Use logarithm rules to move out of the exponent.
Step 6
Logarithm base of is .
Step 7
Multiply by .
Step 8
Rewrite using the change of base formula.
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Step 8.1
The change of base rule can be used if and are greater than and not equal to , and is greater than .
Step 8.2
Substitute in values for the variables in the change of base formula, using .
Step 9
The result can be shown in multiple forms.
Exact Form:
Decimal Form: