Question

If 2to the power x-1+2to the power x+1=320

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Answer 1

$2^{x-1}+2^{x+1}=320$

We know that :

$2^{x-1}=2^x*2^{-1}$ and $2^{-1}=\frac{1}{2}$

$2^x*2+\frac{2^x}{2} =320$

Multiply 2 to both sides, and let $2^x=t$ for convenience.

$4t+t=640$

$t=128$

Substitute $t=2^x$.

$2^x=128$

∴ $x=7$

Answer 2

Answer:

The value of x is 7.

Step-by-step explanation:

We have been given the equation

The exponent rule:

Using these properties, we have

On simplifying, we get

Take 2^x common

Divide both sides by 1+4 = 5

Now, we can write 2^7=128

Thus, the value of x is 7