Govt. Exams
Entrance Exams
# Solving Exponential Equations
To solve exponential equations, express both sides as powers of the same base, then equate the exponents.
Step 1: Express 32 as a Power of 2
We need to rewrite the right side of the equation using base 2, since the left side already has base 2.
(because \(2 \times 2 \times 2 \times 2 \times 2 = 32\))
Step 2: Equate the Exponents
Now substitute this into the original equation and use the property that if \(a^m = a^n\), then \(m = n\).
The value of x is 4.
Answer: (B) 4
Factors of 48: 1,2,3,4,6,8,12,16,24,48. Factors of 64: 1,2,4,8,16,32,64. HCF = 16.
4³ = 64, 2⁻² = 1/4. Therefore, 64 × 1/4 = 16.
3x - 7 = 2 → 3x = 9 → x = 3.
Sum of interior angles = (n - 2) × 180° where n = 8. So (8 - 2) × 180° = 6 × 180° = 1080°.
If sin θ = 3/5, then in a right triangle, opposite = 3, hypotenuse = 5. Using Pythagoras, adjacent = 4. Therefore, cot θ = adjacent/opposite = 4/3.
12 = 2²×3, 18 = 2×3². LCM = 2²×3² = 36
Perimeter = 2(l+b), 28 = 2(8+b), 14 = 8+b, b = 6 cm
f'(x) = d/dx(3x² + 2x + 1) = 6x + 2
a² + b² = (a+b)² - 2ab = 100 - 42 = 58
