Solving Exponential and Logarithmic Equations — Quiz
Question 7 • Mathematics III
What is the value of x if 9 raised to the x minus 1 power minus 2 is equal to 25 ?
Answer
A
x is equal to 2
B
x is equal to 5 halves
C
x is equal to 1 half
D
x is equal to 4
Explanation
Add 2 to both sides: 9^(x − 1) = 27. Since 9 = 3² and 27 = 3³, we have (3²)^(x − 1) = 3³, so 2(x − 1) = 3. Solving gives x = 5/2, or five halves, which is choice B.
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