Question

find the value of x if 4^x = 64
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Answer 1

$\sf{Answer}$

Solution:-

Step by step explanation:-

Given ,

4^x = 64

64 Can be written as

Factorized form of 64 =

64 = 2× 32

64 = 2 × 2 × 16

64 = 2 × 2 × 2 ×8

64 = 2×2×2×2×4

64 = 2 × 2 × 2 ×2 × 2 ×2

64 = 2⁶

So, factorised form of 64 = 2⁶

4^x = 2⁶

Bases are not equal

So, convert 4^x in terms of 2

(2)²×x = 2⁶

2^2x = 2⁶

Bases are equal

hence powers should be equal

2x = 6

x = 6/2

x = 3

So, value of x is 3

Verification:

Substuite value of x It should be equal to 64

x = 3

4^x = 64

4³ = 64

4 × 4 × 4 = 64

64 = 64

_______________________________

Hence verified !

So, value of x is 3

Answer 2

$\huge \sf \bf\color{purple}\underline{\underline{Answer}} :$

$\large x= 3$

$\huge \sf \bf\color{purple}\underline{\underline{Solution}} :$

Factors of 64

• 64 = 2 × 2 × 2 ×2 × 2 ×2

Factors of 4

• 4 = 2×2

so, we can write it as ,

$\large \sf 4^{x} =64 \\ \\ \large \sf ⟹2^{2x}=2⁶$

Bases are same , hence their Powers will be equal .

⟹ 2x=6

$\sf \large⟹ x= \frac{\cancel{6}}{\cancel{2}} \\ \\ \sf ⟹x= 3$