Question

Find the value of x, if 2^ (2 X + 1 )+ 4 ^(x + 1 )- 384 =0

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The value of x is 3

Solution:

Given that,

$2^{2x+1} + 4^{x+1} - 384 = 0$

Use the following law of exponent

$a^{m + n} = a^m \times a^n$

Therefore,

$2^{2x} \times 2^1 + 4^{x+1} - 384 = 0\\\\Also\\\\2^{2x} \times 2^1 + (2^2)^{x+1} - 384 = 0\\\\Similarly\ use\ law\ of\ exponent\\\\(2^{2x} \times 2^1) + (2^{2x} \times 2^2) -384=0$

$Divide\ throughtout\ by\ 2\\\\2^{2x} + 2^{2x } \times 2 - 192 = 0\\\\2^{2x} + 2^{2x } \times 2 = 192\\\\Take\ 2^{2x}\ as\ common\\\\2^{2x}(1+2) = 192\\\\2^{2x} \times 3 = 192\\\\2^{2x} = \frac{192}{3}\\\\2^{2x} = 64\\\\64\ can\ rewritten\ as\ 2^6\\\\2^{2x} = 2^6\\\\When\ base\ is\ same\ powers\ can\ be\ equated\\\\2x = 6\\\\x = 3$

Thus value of x is 3

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