Find the value of ‘x’ if (16)3x – 7 × (2)8x = (4)9x – 2 × (8)2 – x.
1). 2
2). 4
3). 6
4). 8
Given,
⇒ (16)3x – 7 × (2)8x = (4)9x – 2 × (8)2 – x
⇒ (24)3x – 7 × (2)8x = (22)9x – 2 × (23)2 – x
⇒ (2)12x – 28 × (2)8x = (2)18x – 4 × (2)6 – 3x
⇒ (2)12x – 28 + 8x = (2)18x – 4 + 6 – 3x
⇒ (2)20x – 28 = (2)15x + 2
Equating powers of 2,
⇒ 20x – 28 = 15x + 2
⇒ 20x – 15x = 28 + 2
⇒ 5x = 30
∴ x = 30/5 = 61. $\left(\sqrt[3]{1000}+\sqrt[3]{0.008}-\sqrt[3]{0.125}\right)$ is equal to :
3. What should come in place of question mark (?) in the following question? 361 × 350 ÷ 70 = 25 × ?
4. Find the value of [(525 + 252)2 – (525 – 252)2]/(525 × 252).
7. The square root of a positive number less than 100 lies between :