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Subjects
Class 10MathematicsPolynomialsOperations on real numbers and the laws of exponentsExpertLevel 43
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If (3^{x}\cdot9^{x-1}=243), what is the value of (x)?

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Answer and explanation

Correct answer: (\frac{7}{3})

Since (9^{x-1}=3^{2x-2}), the total exponent is (x+2x-2=3x-2). From (243=3^{5}), (3x-2=5), so (x=\frac{7}{3}).

Related tags

Exponent EquationCommon BasePowers

Frequently asked questions

What is the correct answer to this question?

(\frac{7}{3})

Why is this the correct answer?

Since (9^{x-1}=3^{2x-2}), the total exponent is (x+2x-2=3x-2). From (243=3^{5}), (3x-2=5), so (x=\frac{7}{3}).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.

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