Question

2^x+1 + 2^x-1 =640.find the value of 2^x with formula

Answer 1

Answer:

Answer:

The value of x is 8.

Given:

The equation is,

2^x+1+2^x-1=640

2^x.2+2^x/2=640

2^x(2+1/2)=640

2^x(5/2)=640

2^x(1/2)=128

2^x=256

2^x=2⁸

x=8

So the value of x is 8....

Step-by-step explanation:

Hope it helps you......

Answer 2

Answer:

Step-by-step explanation:

Concept:

The concept of indices will help us to solve the given question.The little floating number that follows a number or letter is called an index, or power. Indicators display the number of times a letter or number has been multiplied by itself. Maths. Number.

Given:

The expression  is $2^{x+1} +2^{x-1} =640$ which is given in the question.

To Find:

We need to find out the value of $2^{x}$ .

Solution:

According to the law of indices , we can write one formula as $a^{m} \times a^{n}=a^{m+n}$ .

Here the expression is $2^{x+1} +2^{x-1} =640$ .

Using the above formula we can write $2^{x} \times 2^{1} +2^{x} \times 2^{-1}=640$

First solve the L.H.S.

Take $2^{x}$ from the L.H.S $2^{x} (2+2^{-1})$

Now we can write $2^{x} (2+2^{-1})= 2^{x} (2+\frac{1}{2} )=2^{x} \times \frac{5}{2}$

The expression will be $2^{x} \times \frac{5}{2}=640$ .

Take the $\frac{5}{2}$ to the R.H.S.

$2^{x} =640 \times \frac{2}{5} =256$

Therefore, the value of $2^{x}$ is $256$ .

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