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11111nata11111 [884]
3 years ago
11

Pls answer this...its very important for me...i have an exam coming up...and this 2 questions will come up so pls help. I WILL M

ARK AS BRAINLIEST WHOEVER ANSWERED RIGHT.
1. Find the value of x
a) \frac{4^{2x} }{4^{x} } = 64
b) (2^{2x} )^{3} = 64
Mathematics
1 answer:
tamaranim1 [39]3 years ago
3 0

Answer:

a. x = 3

b. x = 3

Step-by-step explanation:

Given

\frac{4^{2x}}{4^x} = 64

(2^{2x}) = 64

Required

Find x

Solving \frac{4^{2x}}{4^x} = 64

From laws of indices;

\frac{a^{m}}{a^n} = a^{m-n}

So;

4^{2x-x} = 64

4^{x} = 64

Write 64 in base of 4

4^{x} = 4^3

From laws of indices;

if\ x^a = x^b;\ then\ a = b

So; x = 3

Solving (2^{2x}) = 64

Write 64 as a base of 2

(2^{2x}) = 2^6

if\ x^a = x^b;\ then\ a = b

2x = 6

Divide both sides by 2

\frac{2x}{2} = \frac{6}{2}

x = 3

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