I need help solving these equations!?

Question

1.) sqrt(4^x) - 5 = 0
2.) x^(3) - 2^(2x) = 0

Answer 1

1) Given equation is sqrt(4^x) - 5 = 0

                               => sqrt(4^x) = 5

                               => 4^x = 25     ->(1)                 [By squaring on both sides]

     Applying logarithm on both sides we get,

                          log4^x = log25

                    => xlog4 = log5^2

                    => xlog4 = 2log5

                    => x/2 = log5 / log4                            [Since log5 = 0.6989, log4 = 0.6020]                

                                = 0.6989 / 0.6020

                                = 1.1609

                    => x = 2*1.1609

                            = 2.3238

If we substitute x value in (1) we get,

                        4^2.3238 = 25.06

                                        = 25

Therefore x = 2.3238