Question

If 4^{x + 3} = 112 + 8 × 4^x, find the value of (18x)^3x.

Answer 1

4^{x + 3} = 112 + 8 × 4^x 
⇒ 4^x x 4³ = 112 + 8 x 4^x 
⇒  64 x 4^x = 112 + 8 x 4^x 
Let 4^x = y
64y = 112 + 8y
⇒ 56y = 112
⇒ y = 2
Substituting We get,
4^x = 2
⇒ 2^2x = 2
⇒ 2x = 1
⇒ x = `1/2`

`( 18x )^(3x)  = (18/2)^( 3 xx 1/2 ) = 9^( 3 xx 1/2 ) = ( 9^(1/2))^3 = 3^3 = 27`