Question

1/16^3x=64^2(x+8)
Solve for x.

Answer 1

x = -4

Explanation:

16 = 4*4 = 4²

64 = 4 * 4* 4 = 4³

`((1)/(16))^(3x)=64^(2*(x+8))\\\\\\(16^(-1))^(3x)=64^(2x + 16)\\\\\\16^(-3x)=64^(2x +16)\\\\(4^(2))^(-3x)=(4^(3))^(2x+16)\\\\4^(-6x)=4^(6x +48)`

As bases are same, compare exponents

6x + 48 = -6x

Subtract 48 from both sides

6x = -6x - 48

Add '6x' to both sides

6x + 6x = -48

12x = -48

Divide both sides by 12

x = -48/12

x = -4