Answer:
x = [tex]\frac{11}{7}[/tex]
Step-by-step explanation:
note that 64 = [tex]2^{6}[/tex] and 32 = [tex]2^{5}[/tex] , thus
[tex](2^{6}) ^{2x-1}[/tex] = [tex](2^{5}) ^{x+1}[/tex] , that is
[tex]2^{6(2x-1)}[/tex] = [tex]2^{5(x+1)}[/tex]
[tex]2^{12x-6}[/tex] = [tex]2^{5x+5}[/tex]
Since the bases on both sides are equal, then equate the exponents
12x - 6 = 5x + 5 ( subtract 5x from both sides )
7x - 6 = 5 ( add 6 to both sides )
7x = 11 ( divide both sides by 7 )
x = [tex]\frac{11}{7}[/tex]
