Math Problem Statement
Solve each equation for x by applying properties of exponents and logarithms. log3(3x+6)/log3(81) = 1.
Solution
To solve this equation:
we apply the properties of logarithms step by step:
Step 1: Simplify
We know that , so:
The equation now becomes:
Step 2: Eliminate the denominator
Multiply through by 4 to eliminate the denominator:
Step 3: Rewrite in exponential form
Using the property , rewrite the logarithmic equation:
Simplify :
Step 4: Solve for
Subtract 6 from both sides:
Divide by 3:
Final Answer:
Let me know if you'd like further clarification!
Related Questions:
- What are the general properties of logarithms used here?
- How do you rewrite logarithmic equations in exponential form?
- Why is ? Explain step-by-step.
- Can the solution be verified? If so, how?
- What would the equation look like if ?
Tip:
Always check your solutions by substituting back into the original equation to verify correctness.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Logarithms
Exponential Equations
Properties of Logarithms
Formulas
log_b(a) = c implies b^c = a
log_b(b^n) = n
Theorems
Change of Base Property for Logarithms
Exponential-Logarithmic Relationship
Suitable Grade Level
Grades 9-11