Math Problem Statement
Solution
Let's solve each part of question 26 by finding the value of that satisfies the given equations.
Part (i)
The equation given is:
Step-by-Step Solution
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Combine the terms on the left side:
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Rewrite as :
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Equate the exponents since the bases are the same:
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Solve for :
So, the value of for part (i) is:
Part (ii)
The equation given is:
Step-by-Step Solution
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Simplify the left side: So,
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Equate the exponents since the bases are the same:
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Solve for :
So, the value of for part (ii) is:
Summary
- For part (i),
- For part (ii),
Would you like a more detailed explanation of any step or have questions about these solutions?
Related Questions
- How would you solve equations with variables in both the base and exponent?
- What properties of exponents are used when solving exponential equations like these?
- How can we simplify expressions involving fractional exponents?
- Why does the base need to be the same when equating exponents?
- What are some real-world applications of exponential equations?
Tip
When simplifying exponent expressions, always look for common bases, as it allows you to equate the exponents and solve for unknowns.
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Math Problem Analysis
Mathematical Concepts
Exponents
Algebraic Equations
Exponent Laws
Formulas
(a^m) × (a^n) = a^(m+n)
(a^m)^n = a^(m*n)
Theorems
Laws of Exponents
Suitable Grade Level
Grades 9-10