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exponent_equations MCQ Questions for Class 10

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6 questions tagged with exponent_equations.

Question 1/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(\frac{2^{x}\cdot2^{x+2}}{2^{3}}=32\), तो (x) का मान क्या है?

If \(\frac{2^{x}\cdot2^{x+2}}{2^{3}}=32\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

The total exponent on the left is (x+x+2-3=2x-1), and \(32=2^{5}\), so (2x-1=5), giving (x=3). In exams, convert the whole expression into one power.

Step 2

Why this answer is correct

The correct answer is B. (3). The total exponent on the left is (x+x+2-3=2x-1), and \(32=2^{5}\), so (2x-1=5), giving (x=3). In exams, convert the whole expression into one power.

Step 3

Exam Tip

बाएँ पक्ष की कुल घात (x+x+2-3=2x-1) है, और \(32=2^{5}\), इसलिए (2x-1=5) से (x=3)। परीक्षा में पूरी अभिव्यक्ति को एक ही घात में बदलें।

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Question 2/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(4^{x}=2^{10}\), तो (x) का मान क्या होगा?

If \(4^{x}=2^{10}\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (5)

Step 1

Concept

Since (4^{x}=\(2^{2}\)^{x}=2^{2x}), (2x=10) and (x=5). In exams, convert mixed bases into a common base.

Step 2

Why this answer is correct

The correct answer is B. (5). Since (4^{x}=\(2^{2}\)^{x}=2^{2x}), (2x=10) and (x=5). In exams, convert mixed bases into a common base.

Step 3

Exam Tip

(4^{x}=\(2^{2}\)^{x}=2^{2x}), इसलिए (2x=10) और (x=5)। परीक्षा में मिश्रित आधार को समान आधार में बदलें।

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Question 3/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(2^{a}=8\) और \(3^{b}=81\), तो \(a^{b}\) का मान क्या है?

If \(2^{a}=8\) and \(3^{b}=81\), what is the value of \(a^{b}\)?

Explanation opens after your attempt
Correct Answer

C. (81)

Step 1

Concept

From \(2^{a}=2^{3}\), (a=3), and from \(3^{b}=3^{4}\), (b=4), so \(a^{b}=3^{4}=81\). In exams, compare powers using equal bases.

Step 2

Why this answer is correct

The correct answer is C. (81). From \(2^{a}=2^{3}\), (a=3), and from \(3^{b}=3^{4}\), (b=4), so \(a^{b}=3^{4}=81\). In exams, compare powers using equal bases.

Step 3

Exam Tip

\(2^{a}=2^{3}\) से (a=3) और \(3^{b}=3^{4}\) से (b=4), इसलिए \(a^{b}=3^{4}=81\)। परीक्षा में घातों की तुलना समान आधार पर करें।

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Question 4/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(5^{x}=125\) और \(2^{y}=32\), तो (x+y) का मान क्या है?

If \(5^{x}=125\) and \(2^{y}=32\), what is the value of (x+y)?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

Since \(125=5^{3}\), (x=3), and since \(32=2^{5}\), (y=5), so (x+y=8). In exams, write numbers as powers of their prime bases.

Step 2

Why this answer is correct

The correct answer is C. (8). Since \(125=5^{3}\), (x=3), and since \(32=2^{5}\), (y=5), so (x+y=8). In exams, write numbers as powers of their prime bases.

Step 3

Exam Tip

\(125=5^{3}\) से (x=3) और \(32=2^{5}\) से (y=5), इसलिए (x+y=8)। परीक्षा में संख्याओं को उनके मूल आधार की घात में लिखें।

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Question 5/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि \(2^{x+1}+2^{x}=48\), तो (x) का मान क्या है?

If \(2^{x+1}+2^{x}=48\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

Here \(2^{x+1}+2^{x}=2\cdot2^{x}+2^{x}=3\cdot2^{x}=48\), so \(2^{x}=16=2^{4}\). In exams, factor the common power \(2^{x}\).

Step 2

Why this answer is correct

The correct answer is B. (4). Here \(2^{x+1}+2^{x}=2\cdot2^{x}+2^{x}=3\cdot2^{x}=48\), so \(2^{x}=16=2^{4}\). In exams, factor the common power \(2^{x}\).

Step 3

Exam Tip

\(2^{x+1}+2^{x}=2\cdot2^{x}+2^{x}=3\cdot2^{x}=48\), इसलिए \(2^{x}=16=2^{4}\)। परीक्षा में सामान्य घात \(2^{x}\) बाहर लें।

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Question 6/6 Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (\left\(3^{x}\right\)^{2}=729), तो (x) का मान क्या है?

If (\left\(3^{x}\right\)^{2}=729), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

We have (\left\(3^{x}\right\)^{2}=3^{2x}) and \(729=3^{6}\), so (2x=6) and (x=3). In exams, rewrite both sides with the same base.

Step 2

Why this answer is correct

The correct answer is B. (3). We have (\left\(3^{x}\right\)^{2}=3^{2x}) and \(729=3^{6}\), so (2x=6) and (x=3). In exams, rewrite both sides with the same base.

Step 3

Exam Tip

(\left\(3^{x}\right\)^{2}=3^{2x}) और \(729=3^{6}\), इसलिए (2x=6) और (x=3)। परीक्षा में दोनों पक्षों को समान आधार में लिखें।

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