Answer:
a. x = 3
b. x = 3
Step-by-step explanation:
Given
[tex]\frac{4^{2x}}{4^x} = 64[/tex]
[tex](2^{2x}) = 64[/tex]
Required
Find x
Solving [tex]\frac{4^{2x}}{4^x} = 64[/tex]
From laws of indices;
[tex]\frac{a^{m}}{a^n} = a^{m-n}[/tex]
So;
[tex]4^{2x-x} = 64[/tex]
[tex]4^{x} = 64[/tex]
Write 64 in base of 4
[tex]4^{x} = 4^3[/tex]
From laws of indices;
[tex]if\ x^a = x^b;\ then\ a = b[/tex]
So; x = 3
Solving [tex](2^{2x}) = 64[/tex]
Write 64 as a base of 2
[tex](2^{2x}) = 2^6[/tex]
[tex]if\ x^a = x^b;\ then\ a = b[/tex]
[tex]2x = 6[/tex]
Divide both sides by 2
[tex]\frac{2x}{2} = \frac{6}{2}[/tex]
[tex]x = 3[/tex]
