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

Answer:(b)

$2^{x - 1} + 2^{x + 1}$ = 320

$2^{x-1}(1+ 2^2) = 320$

$2^{x-1} ×5 =320$

$2^{x-1}= 320/5 =64 ⇒2^{x -1} = 2^{6}$

$x - 1 = 6 ⇒ x = 7$

Answer:(b)

$x^2 - √3$ = 0

$x^2-(3)^{1/2}=0$

$x^2-(3^{1/4})^2=0$

$(x+3^{1/4})(x-3^{1/4})=0$

$x=3^{1/4} or {-3}^{1/4}$

Product of roots

$=3^{1/4}×-3^{1/4}=-√3$

Note : Product of the roots of $ax^2+bx+c=0 is c/a$

Product of the roots of $x^2-b. 0-√3=0 is -√3$

Answer:(c)

$(3/4)^×3(4/3)^{-7}= (3/4)^{2x}$

$(3/4)^3×(3/4)^{7}= (3/4)^{2x}$

$(3/4)^10=(3/4)^{2x}$

2x=10⇒ x=5

Answer:(a)

$[√^3{√^6{√{5^9}}}]^4[√^3{√^6{√{5^9}}}]^4$

=$[5^{9×1/6×1/3}]^4[5^{9×1/6×1/3}]^4$

=$[5^{1/2×4}][5^{1/2×4}]=5^2×5^2=5^4$

Answer:(b)

$(2^3)^2=(2^2)^x$

$2^6 = 2^{2x}$ ⇒ 2x = 6

$x = 6/2$ = 3

$3^x = 3^3 = 3 × 3 × 3 = 27$

Answer:(d)

$5√5 ×5^3 ÷5^{-3/2}= 5^{a+2}$

$5 × 5^{1/2} × 5^3 ÷ 5^{-3/2} = 5^{a + 2}$

$5^{1+ 1/2 +3+ 3/2} = 5^{a + 2}$

$5^6 = 5^{a + 2}$ ⇒ a + 2 = 6

a = 6 - 2 = 4

$[a^m × a^n = a^{m + n},]$

$[a^m ÷ a^n = a^{m - n}]$