Solve the equations

Question

100^(2x+4) =1000^(x+4)

Answer 1

The equation

100^(2x + 4)   =   1000^(x + 4)

[10^2]^(2x + 4)   =   [10^3]^(x + 4)

10^[2(2x + 4]   =   10^[3(x + 4)]              [ Since (a^m)^n) =  a^(mn) ]

As the bases are same equate the exponents

2(2x + 4)   =   3(x + 4)

4x + 8   =   3x + 12

4x - 3x   =   12 - 8

x  =  4