Question

Solve 2 to power x+1 + 2 to power x+ 2 =192​

Answer 1

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Given:

• $2^{x+1} + 2^{x+2} = 192$

To Find:

• Value of x

Solution:

$\longrightarrow 2^{x+1} + 2^{x+2} = 192 \\:\implies 2^{x+1} + 2^{x+1}*2 = 192 \\:\implies</p><p>2^{x+1}(1 + 2) = 192 \\:\implies 2^{x+1} = 64 \\:\implies 2^x * 2 = 64 \\:\implies 2^x = 32 \\:\implies 2^x = 2^5 \\\bf{:\implies x = 5}$

hope it helps!

Answer 2

Answer:

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)

Thanks!!