Precalculus Examples

Write as a Single Logarithm 15 log base 3 of cube root of x+ log base 3 of 15x^9- log base 3 of 15
Step 1
Use the quotient property of logarithms, .
Step 2
Simplify each term.
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Step 2.1
Simplify by moving inside the logarithm.
Step 2.2
Rewrite as .
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Step 2.2.1
Use to rewrite as .
Step 2.2.2
Apply the power rule and multiply exponents, .
Step 2.2.3
Combine and .
Step 2.2.4
Cancel the common factor of and .
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Step 2.2.4.1
Factor out of .
Step 2.2.4.2
Cancel the common factors.
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Step 2.2.4.2.1
Factor out of .
Step 2.2.4.2.2
Cancel the common factor.
Step 2.2.4.2.3
Rewrite the expression.
Step 2.2.4.2.4
Divide by .
Step 2.3
Cancel the common factor of .
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Step 2.3.1
Cancel the common factor.
Step 2.3.2
Divide by .
Step 3
Use the product property of logarithms, .
Step 4
Multiply by by adding the exponents.
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Step 4.1
Use the power rule to combine exponents.
Step 4.2
Add and .