Questions & Answers: "Indices and Roots"

Complete guide to "Indices and Roots" for Math students. Below you will find important questions and model answers to help you prepare.

1 Questions

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We are building a dedicated quiz for this topic, but you can test your skills on a similar concept: Geometry (Angles, Circles, and 3D Nets) - Scholarship-VIII Practice Set 1.

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Question 1

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Find the value of x, if $3^{x}+3^{x+1}=108$

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Explanation

Given the equation $3^x + 3^{x+1} = 108$ . We can rewrite $3^{x+1}$ as $3^x \cdot 3^1$ . So, the equation becomes $3^x + 3^x \cdot 3 = 108$ . Factor out $3^x$ : $3^x(1 + 3) = 108$ . This simplifies to $3^x(4) = 108$ . Divide by $4$ : $3^x = \frac{108}{4} = 27$ . Since $27 = 3^3$ , we have $3^x = 3^3$ . Therefore, $x = 3$ .

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