1 Crore+ students have signed up on EduRev. Have you? 
Let (17)^{3.5} x (17)^{x} = 17^{8}
Then, (17)^{3.5 + x} = 17^{8}
∴ 3.5 + x = 8
⇒ x = (8  3.5)
⇒ x = 4.5
If (a / b)^{x  1} = (b / a)^{x  3} , then the value of x is:
Given:
⇒ (a / b)^{x  1} = (b / a)^{x  3}
⇒ (a / b) ^{x  1} = (b / a) ^{(x  3)} = (a / b)^{(3  x)}
⇒ x  1 = 3  x
⇒ 2x = 4
⇒ x = 2
Given that 10^{0.48} = x, 10^{0.70} = y and x^{z} = y^{2}, then the value of z is close to:
⇒ x^{z} = y^{2} ⇔ 10^{(0.48 z)} = 10^{(2 x 0.70)} = 10^{1.40}
⇒ 0.48 z = 1.40
⇒ z = 140 / 48 = 35 / 12 = 2.9(approx.)
⇒ 5^{a} = 3125 ⇔ 5^{a} = 5^{5}
⇒ a = 5.
∴ 5^{(a  3)} = 5^{(5  3) }= 5^{2} = 25.
If 3^{(x  y)} = 27 and 3^{(x + y)} = 243, then x is equal to:
⇒ 3^{x  y} = 27 = 3^{3} ⇔ x  y = 3 ....(i)
⇒ 3^{x + y} = 243 = 3^{5} ⇔ x + y = 5 ....(ii)
On solving (i) and (ii), we get x = 4.
⇒ (256)^{0.16} x (256)^{0.09} = (256)^{(0.16 + 0.09)}
= (256)^{0.25}
= (256)^{(25 / 100)}
= (256)^{(1 / 4)}
= (4^{4})^{(1 / 4)}
= 4^{4}^{(1 / 4)}
= 4^{1}
= 4
⇒ (10)^{150} ÷ (10)^{146} = 10^{150} / 10^{146}
= (10)^{150} ^{146}
= 10^{4}
= 10000.
1/(1 + x^{(b  a) }+ x^{(c  a)}) + 1/(1 + x^{(a  b)} + x^{(c  d)}) + 1/(1 + x^{(b  c)} +x^{(a  c) }) = ?
Given Exp:
1/(1 + x^{b} / x^{a} + x^{c} / x^{a}) + 1/(1 + x^{a} / x^{b} + x^{c} / x^{b}) + 1/(1 + x^{b} / x^{c} +x^{a} / x^{c})
= x^{a}/(x^{a} + x^{b} + x^{c} ) + x^{b}/(x^{a} + x^{b} + x^{c} ) + x^{c}/(x^{a} + x^{b} + x^{c} )
= (x^{a} + x^{b} + x^{c} ) / (x^{a} + x^{b} + x^{c} )
= 1.
Let (25)^{7.5} x (5)^{2.5} ÷ (125)^{1.5} = 5^{x}.
Then, (5^{2})^{7.5} x 5^{2.5} / (5^{3}) ^{1.5} = 5^{x}
⇒ (5^{2})^{7.5} x 5^{2.5} / (5)^{3 x} ^{1.5} = 5x
⇒ 5^{15} x 5^{2.5} / 5^{4.5} = 5^{x}
⇒ 5^{x} = 5^{(15 + 2.5  4.5)}
⇒ 5^{x} = 5^{13}
∴ x = 13.
⇒ (0.04)^{1.5} = (4 / 100)^{1.5}
= (1 / 25) ^{(3 / 2)}
= (5^{2})^{(3 / 2)}
= (5)^{2 x (3 / 2)}
= 5^{3}
= 125.
163 videos163 docs131 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
163 videos163 docs131 tests









