BackLogarithmic Expressions and Applications – Precalculus Study Guidance
Study Guide - Smart Notes
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Q1. Express log6 216 = 3 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your understanding of how to convert a logarithmic equation to its equivalent exponential form.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Step-by-Step Guidance
Identify the base (), the argument (), and the result () in the logarithmic equation.
Recall that means raised to the power equals .
Write the equivalent exponential equation using the identified values.
Try solving on your own before revealing the answer!
Final Answer:
We converted the logarithmic equation to exponential form by raising the base to the exponent.
Q2. Express log3 81 = 4 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your ability to convert logarithmic equations to exponential equations.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Step-by-Step Guidance
Identify the base (), argument (), and exponent () in the logarithmic equation.
Recall the conversion: is equivalent to .
Write the exponential equation using these values.
Try solving on your own before revealing the answer!
Final Answer:
The logarithmic equation was rewritten in exponential form.
Q3. Express log3 (1/9) = −2 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your ability to convert logarithmic equations with negative exponents to exponential form.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Step-by-Step Guidance
Identify the base (), argument (), and exponent ().
Recall that a negative exponent means the reciprocal: .
Write the exponential equation using these values.
Try solving on your own before revealing the answer!
Final Answer:
Negative exponents indicate reciprocals in exponential form.
Q4. Express log64 8 = 1/2 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your understanding of fractional exponents in logarithmic and exponential forms.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Fractional exponents: means the square root of .
Step-by-Step Guidance
Identify the base (), argument (), and exponent ().
Recall that is the square root of .
Write the exponential equation using these values.
Try solving on your own before revealing the answer!
Final Answer:
Fractional exponents represent roots in exponential form.
Q5. Express log7 = 0.845 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your ability to convert logarithmic equations with decimal exponents to exponential form.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Step-by-Step Guidance
Identify the base (), argument (), and exponent ().
Recall the conversion: is equivalent to .
Write the exponential equation using these values.
Try solving on your own before revealing the answer!
Final Answer:
The logarithmic equation was rewritten in exponential form.
Q6. Express log1/2 32 = −5 in exponential form.
Background
Topic: Logarithmic and Exponential Relationships
This question tests your ability to convert logarithmic equations with fractional bases and negative exponents to exponential form.
Key Terms and Formulas
Logarithmic form:
Exponential form:
Negative exponents:
Step-by-Step Guidance
Identify the base (), argument (), and exponent ().
Recall that a negative exponent means the reciprocal.
Write the exponential equation using these values.
Try solving on your own before revealing the answer!
Final Answer:
Negative exponents indicate reciprocals in exponential form.
