Math Problem Statement
Solution
Let me transcribe and solve the equations from the image.
The problems given are:
65)
66)
67)
Solution for each equation:
65)
- First, use the product rule for exponents: .
Now the equation becomes:
Since the bases are the same, equate the exponents:
Divide both sides by :
There seems to be no solution for this equation since it leads to a contradiction. Therefore, no solution.
66)
- Again, use the product rule for exponents:
The equation now becomes:
Since the bases are the same, equate the exponents:
Solve for :
So, the solution is .
67)
- Since the bases are the same, equate the exponents:
Solve for :
So, the solution is .
Summary of Solutions:
- 65) No solution.
- 66)
- 67)
Let me know if you want further details on these solutions or if you have any questions!
Here are 5 related questions to extend your practice:
- Solve: .
- Solve: .
- Solve: .
- Solve: .
- Solve: .
Tip: When solving exponential equations, always check if the bases can be made the same—this is the key to simplifying and equating exponents.
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Math Problem Analysis
Mathematical Concepts
Exponential Equations
Properties of Exponents
Formulas
Product of Powers: a^m * a^n = a^(m+n)
Equating Exponents: If a^m = a^n, then m = n
Theorems
Exponentiation Rules
Suitable Grade Level
Grades 8-10