Question

If 2^x-1 + 2^x+1 = 40, what is the value of x?

Answer 1

Answer:

4

Step-by-step explanation:

2^(x-1) + 2^(x+1) = 40

( 2^(x-1) ) ( 1  + 2^2 ) = 40

( 2^(x-1) ) 5 = 40

2^(x-1)  =  8

2^(x-1)  =  2^3

Therefore

x-1 = 3

x=4

Answer 2

This is simple....

2^(x-1)+2^(x+1)=1280 is the given equation

Consider LHS

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

This can be written as.. (2^x/2)+(2^x*2)

Then taking 2^x as then common factor we get;

2^x{(1/2)+(2)}

Now we get that

2^x[5/2]=1280

So on transposing 5/2 to RHS we get

2^x=512

2^x=2^9

Therefore we get that x=9

Simple!!!

Thanks!!cheers...