Question

if 2^x-1+2^x+1 = 320 then x = ?

Answer 1

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Answer 2

Value of x is 7.

Given:

• ${2}^{x - 1} + {2}^{x + 1} = 320$

To find:

• Find the value of x.

Solution:

Concept to be used:

• If ${a}^{n} = {a}^{m}$, then $n = m$.

Step 1:

Rewrite the given expression.

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

or

take ${2}^{x}$ common.

${2}^{x} ( \frac{1}{2} + 2) = 320$

or

${2}^{x} \times \frac{5}{2} = 320$

or

${2}^{x} = 320 \times \frac{2}{5}$

or

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

or

${2}^{x} = 128$

Step 2:

Write RHS in power notation.

${2}^{x} = {2}^{7}$

or

compare powers; as base are same.

$\bf \red{x = 7 }$

Thus,

Value of x is 7.

Learn more:

1) Simplify : 2 ^n + 2 ^n-1 ÷ 2^n+1 - 2^n.

https://brainly.in/question/6792023

2) in power notation 243/32 can be expressed as

https://brainly.in/question/23672039