Question

if 2 raised to the power 2n-1 equals to 8 raised to the power 3-n then the value of n is​

Answer 1

Hope this will help you..

Answer 2

Answer:

The answer to the given question is the value of n is 2.

Step-by-step explanation:

Given :

If 2 is raised to the power 2n-1 equals 8 raised to the power 3-n

To find :

we have to find the value of n.

Solution :

The given question can be expressed as

${2}^{2n - 1} = {8}^{3 - n}$

The value 8 can be written as

${2}^{2n - 1} = {2}^{3(3 - n)}$

multiplying the terms on the power of the right side

${2}^{2n - 1} = {2}^{9 -3 n}$

Since the base is the same on both sides, we are equating the powers of the exponents

$2n - 1 = 9 - 3n$

By comparing the like terms and adding we get the value then that value should be divided by the coefficient of n, and the value of n is obtained as

$2n + 3n = 9 + 1 \\ 5n = 10 \\ n = \frac{10}{5} \\ n = 2$

The value of n is obtained as 2.

Therefore, the final answer is 2

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