Question
If $(16)^{2x+3} = (64)^{x+3},$ then $4^{2x-2} =$
✓
Answer
We have to find the value of $4^{2x-2}$ provided $(16)^{2x+3} = (64)^{x+3}$
So,
$(16)^{2x+3} = (64)^{x+3}$
$(2^4)^{2x+3} = (2^6)^{x+3}$
$2^{8x+12} = 2^{6x+18}$
Equating 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
$= 4^{2x-2}$
$= 4^{2\times 3-2}$
$= 4^{6-2}$
$= 4^4$
$= 256$
Hence the correct alternative is $b.$
So,
$(16)^{2x+3} = (64)^{x+3}$
$(2^4)^{2x+3} = (2^6)^{x+3}$
$2^{8x+12} = 2^{6x+18}$
Equating 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
$= 4^{2x-2}$
$= 4^{2\times 3-2}$
$= 4^{6-2}$
$= 4^4$
$= 256$
Hence the correct alternative is $b.$
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