Surds and Indices - General Questions (2)

(256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

   = (256)^0.25

   = (256)^(25/100)

   = (256)^(1/4)

   = (4⁴)^(1/4)

   = 4^4(1/4)

   = 4¹

   = 4

3^x - y = 27 = 3³        x - y = 3 ....(i)

3^x + y = 243 = 3⁵        x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.

5^a = 3125        5^a = 5⁵

 a = 5.

 5^{(a - 3)} = 5^{(5 - 3)} = 5² = 25.

x^z = y²        10^(0.48z) = 10^{(2 x 0.70)} = 10^1.40

 0.48z = 1.40

z =	140	=	35	= 2.9 (approx.)
	48		12

Given	a		x - 1	=		b		x - 3
	b					a

a

x - 1

=

a

-(x - 3)

=

a

(3 - x)

b

b

b

 x - 1 = 3 - x

 2x = 4

 x = 2.

Let (17)^3.5 x (17)^x = 17⁸.

Then, (17)^{3.5 + x} = 17⁸.

 3.5 + x = 8

 x = (8 - 3.5)

 x = 4.5