Question

2 with the power (x-1) + 2 (x+1) =320 , then find the value of (x)

Answer 1

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Answer 2

Answer:

The value of x is 7.

Step-by-step explanation:

We have been given the equation

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

The exponent rule:

$x^a\cdotx^b=x^{a+b}\\\\\frac{x^a}{x^b}=a^{a-b}$

Using these properties, we have

$\frac{2^x}{2}+2\cdot2^{x}=320$

On simplifying, we get

$2^x+4\cdot2^x=640$

Take 2^x common

$2^x(1+4)=640$

Divide both sides by 1+4 = 5

$2^x=\frac{640}{5}\\\\2^x=128$

Now, we can write 2^7=128

$2^x=2^7\\\\x=7$

Thus, the value of x is 7.