Real numbers
Grade Class 10
Question:
<p>If 3825 = 3<sup>x</sup> <span class="math-tex">\(\times\)</span> 5<sup>y</sup> <span class="math-tex">\(\times\)</span> 17<sup>z</sup>, then the value of x + y - 2z is:</p>
<p style="display:inline">1</p>
<p style="display:inline">3</p>
<p style="display:inline">0</p>
<p style="display:inline">2</p>
Step-by-Step Solution
Key Concept: The solution involves performing prime factorization of the given integer and comparing the exponents of the corresponding prime bases to solve for the variables.
<p><span class="math-tex">\(3825=3^2 \times 5^2 \times 17\)</span><br />
On comparing<br />
x = 2, y = 2, z = 1<br />
x + y - 2z = 2 + 2 - 2 <span class="math-tex">\(\times\)</span> 1<br />
= 4 - 2<br />
= 2</p>
Correct Answer: D