Question

Resolva as equações exponenciais:
a)(8/125)^2x-1 = (25/4)^2x
b)^3√25^x = √5
c)5^x-1 = 1

Answer 1

a) ( 8 )^2x-1 = (25)^2x
    125                4

[( 2³ )]^2x-1 = [(5²)]^2x  ==> [( 2)³]^2x-1 = [(5)²]^2x 
  5³                   2²                     5                  2

 [( 2)^3]^2x-1 = [(2)^-2]^2x  ==> 6x - 3 = - 4x ==>
    5                     5
6x+4x = 3 => 10x = 3 =>x = 3 
                                            10
=====================================================
b)^3√25^x = √5

3.(25^x)^1/2 = 5^1/2 ==>  3.[((5)^2)^x)]^1/2 = 5^1/2

3.[(5)^2x)]^1/2 = 5^1/2 ==> 3.[(5)^2x/2] = 5^1/2 ==> 3.(5)^x = 5^1/2

as bases são diferentes . V = ∅
============================================
c) 5^x-1 = 1

 5^x-1 = 5^0

x - 1 = 0 ==> x = 1