Question

2^x + 2^x + 2^x = 192

Answer 1

Answer : 6

Explanation :

2^x + 2^x + 2^x = 192

We see same terms in addition, As we know repeated addition can be written as Multiplication. So, We express this as product.

2^x is added three times, So it will be 3 * 2^x which is written in the next step.

=> 3(2^x) =192

3 which is in the product when transferred to other side, goes to denominator

=> 2^ x = 192/3

Since 192/3 equals 64, Hence the next step will be

=> 2^x =64

64 = 2 * 2 * 2 * 2 * 2 * 2 , So it can be written as 2^6. Hence the next step is

=> 2^x = 2^6

By laws of exponents, If a^m = a^n, then m = n.

Hence, We get x=6 ( Final answer)

Answer 2

Answer:

$Value \:of\: x = 6$

Step-by-step explanation:

$Given \: 2^{x}+2^{x}+2^{x}=192$

$\implies 3 \times 2^{x}=192$

$\implies 2^{x}=\frac{192}{3}$

$\implies 2^{x}= 64$

$\implies 2^{x}=2^{6}$

\* By Exponential Law:

$\boxed {If \: a^{m}=a^{n} \implies m=n }$ *\

$\implies x = 6$

Therefore,

$Value \:of\: x = 6$

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