Question

2^x-1+2^x+1=2560. Find the value of x​

Answer 1

Answer:

Answer is 10

2^x-1+2^x+1=2560

2^x-1+2^x-1+2=2560

Apply Law of Algebra

2^x-1+2^x-1*2^2=2560

2^x-1(1+2^2) =2560

2^x-1=2560/5=2*2*2*2*2*2*2*2*2

2^x-1=2^9

x-1=9

Therefore:x=9+1=10

I hope it will help you

Answer 2

The value of x is 10.

Step-by-step explanation:

We are given ,

$2^{x-1} + 2^{x+1} = 2560$

• For solving this question, first we write it in expanded form, such as

        $2^{x}*2^{-1} + 2^{x}* 2^{1} = 2560$

        $2^{x}*\frac{1}{2} + 2^{x} *2=2560$

• Taking $2^{x}$ as common from both terms in L.H.S

         $2^{x} [\frac{1}{2} +2]=2560$

         $2^{x}* \frac{5}{2}=2560$

• Taking $\frac{5}{2}$ from L.H.S to R.H.S and solving equation

       $2^{x}=2560*\frac{2}{5}$

       $2^{x} = 1024$

• As we know, we get  1024 by multiplying 2 to 10 times that is  $2^{10}$ so we can write  $2^{10}$  in place of 1024.

       $2^{x} =2^{10}$

• We can clearly see that base is same on both sides which is 2 and if bases are same then their powers are also same. So we can write it as,

       $x = 10$

So we get the value of x which is 10.