What is the value of $4^{2 x - 2}$ , if $(16)^{2 x + 3} = (64)^{x + 3}$ ?

64

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256

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32

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512

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Solution

The correct option is D $256$
Given, $(16)^{2 x + 3} = (64)^{x + 3}$

We can write 16 as $2^{4}$ and $64 = 2^{6}$

So, $(2^{4})^{2 x + 3} = (2^{6})^{x + 3}$
$(2)^{8 x + 12} = (2)^{6 x + 18}$

So, $8 x + 12 = 6 x + 18$
$8 x - 6 x = 18 - 12$
$2 x = 6$
$x = 3$

We have to find out the value of $4^{2 x - 2}$
Keep the value of $x$
= $4^{2 \times 3 - 2}$
= $4^{6 - 2}$
= $4^{4}$
= $256$

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Similar questions

Q. If (16)^2x+3 =(64)^x+3, then 4^2x-2 =

(a) 64

(b) 256

(c) 32

(d) 512

Q. The lateral surface area of a cube is 256 m². The volume of the cube is
(a) 64 m³
(b) 216 m³
(c) 256 m³
(d) 512 m³

Question 7
The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is:

A) $512 m^{3}$
B) $64 m^{3}$
C) $216 m^{3}$
D) $256 m^{3}$

Question 7
The lateral surface area of a cube is $256 m^{2}$ . The volume of the cube is:

A) $512 m^{3}$
B) $64 m^{3}$
C) $216 m^{3}$
D) $256 m^{3}$

Q. Mark the correct alternative in the following question:

2^{3^{2}} = (a) 64 (b) 32 (c) 256 (d) 512

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What is the value of 42x−2, if (16)2x+3=(64)x+3?

The correct option is D 256Given, (16)2x+3=(64)x+3We can write 16 as 24 and 64=26So, (24)2x+3=(26)x+3(2)8x+12=(2)6x+18 So, 8x+12=6x+18 8x−6x=18−12 2x=6 x=3We have to find out the value of 42x−2Keep the value of x = 42×3−2= 46−2= 44= 256

What is the value of $4^{2 x - 2}$ , if $(16)^{2 x + 3} = (64)^{x + 3}$ ?