F.4 Law of Indics

1. 3^(2x + 1) - 3^x - 4 = 0

3(3^2x) - 3^x - 4 = 0

3[(3^x)^2] - 3^x - 4 = 0

Set y = 3^x

Then

3y^2 - y - 4 = 0, it is a quadratic equation,

(3y - 4)(y + 1) = 0

y = 4/3 or -1

3^x = 4/3 or 3^x = -1 (rejected)

3^x = 4/3

log(3^x) = log(4/3)

xlog3 = log(4/3)

x = log(4/3) / log3


2. 3(3^2x) - 28(3^x) + 9 = 0

3(3^x)^2 - 28(3^x) + 9 = 0

which is a quadratic equation again

(3(3^x) - 1)(3^x - 9) = 0

3^x = 1/3 or 3^x = 9

3^x = 3^(-1) or 3^x = 3^2

x = -1 or 2