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If (9^x=27), find (x).
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Answer and explanation
Correct answer: (\frac{3}{2})
Express both numbers with base 3: (9^x)=(3^2)^x=3^{2x} and 27=3^3. Thus, 3^{2x}=3^3, so 2x=3 and x=\(\frac{3}{2}\). Therefore, option B is correct. Exam tip: In exponential equations, rewrite both sides with the same base and then equate the exponents.
Frequently asked questions
What is the correct answer to this question?
(\frac{3}{2})
Why is this the correct answer?
Express both numbers with base 3: (9^x)=(3^2)^x=3^{2x} and 27=3^3. Thus, 3^{2x}=3^3, so 2x=3 and x=\(\frac{3}{2}\). Therefore, option B is correct. Exam tip: In exponential equations, rewrite both sides with the same base and then equate the exponents.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: Exponents.
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