If (16)2x+3 = (64)x+3, then 42x-2 = - Vidyadip

MCQ

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

A
64
B
256
C
32
D
512

✓

Answer

256
Solution:
We have to find the value of 4^2x-2 provided (16)^2x+3 = (64)^x+3So,
(16)^2x+3 = (64)^x+3(2⁴)^2x+3 = (2⁶)^x+32^8x+12 = 2^6x+18Equating the power of exponents we get
8x +12 = 6x +18
8x - 6x = 18 - 12
2x = 6
$\text{x}=\frac{6}{2}$
x = 3
The value of 4^2x-2 is
= 4^2x-2= 4^2×3-2= 4^6-2= 4⁴= 256
Hence the correct alternative is b.

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