model 3 based on positive and negative exponent Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer:(a)

$√{3^n}$ = 2187

$3^{n/2} = (3)^7$

$n/2$ = 7

n = 2 × 7 = 14

Answer:(b)

$3^{x+8} = 27^{2x+1}$

$3^{x+8} = (3)^{3(2x+1)}$

x + 8 = 6x + 3

5x = 5 ∴ x=1

Answer:(c)

Unit's digit in the expansion of $(252)^126$

= $2^2$ = 4 (Remainder on dividing 126 by 4 = 2)

Unit's digit in the expansion of $(244)^152$ = 6

Unit's digit in the expansion of $252^126 + 244^152$ = 0

Required remainder = 0

Answer:(d)

$7^1 = 7, 7^2 = 49, 7^3$ = 343,

$7^4 = 2401, 7^5$ = 16807

i.e. after index 4, the unit's digit is repeated.

On dividing 153 by 4, remainder = 1

Unit's digit in the expansion of $(2467)^153=7^1$=7 and unit's digit in the expansion of $(341)^72$ = 1

Required unit's digit = 7 × 1 = 7

Answer:(d)

$3^34 = (3^2)^17 = 9^17$

$2^51 = (2^3)^17 = 8^17$

$7^17 = 7^17$

Clearly, $9^17 > 8^17 > 7^17$

i.e., $3^34 > 2^51 > 7^17$

Answer:(b)

$2^{x+4} - 2^{x+2}$ = 3

$2^{x+2}(2^2 - 1)$ = 3

$2^{x+2}$× 3 = 3

$2^{x+2}$ = 1 = 2°

x + 2 = 0 ⇒ x = - 2