Math Problem Statement
Solve for x
Solution
Let's go through each of the problems step by step to solve for .
6)
We start by expressing the bases as powers of 2: Rewriting the equation: Simplifying: This gives: Solving for :
7)
Express as : Simplifying: This gives: Now, we can equate the exponents: Solving for :
8)
Express the bases in terms of powers of 6: Rewriting the equation: Simplifying: Equating the exponents: Solving for :
9)
Express 81 and 9 as powers of 3: Rewriting the equation: Simplifying: Equating the exponents: Solving for :
10)
Express 32 and 128 as powers of 2: Rewriting the equation: Simplifying: Equating the exponents: Solving for :
Final Answers:
Let me know if you'd like further details on any of these steps!
Here are 5 additional questions for further exploration:
- Can you solve exponential equations using logarithms?
- How do you handle inequalities when solving exponential equations?
- What happens if the bases of the exponential equations are not powers of the same number?
- Can you solve exponential equations with negative exponents?
- How would you graph exponential inequalities?
Tip: Always look for common bases in exponential equations to simplify solving!
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Math Problem Analysis
Mathematical Concepts
Exponential equations
Logarithmic inequalities
Properties of exponents
Simplifying expressions
Formulas
a^x = a^y implies x = y
Exponent rules: (a^m)^n = a^(m*n)
Logarithmic inequality solving: a^x > b implies x > log_b(a)
Theorems
Exponentiation with same base
Logarithmic inequalities
Exponentiation rules for simplifying
Suitable Grade Level
Grades 9-12
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