Question

Solve the following equation.Please help with this question and show working

Answer 1

x = 1

Explanation:

1. Expand the expression:
`2^x * 2^3 = 2*2^(-x) + 15`

2. Evaluate the power:
`2^x * 8 = 2 * (1)/(2^(x)) +15`

3. Substitute. Let's use t for
`2^x` :
`t * 8 = 2 * (1)/(t) +15`

4. Solve for t :

`8t = (2)/(t) + 15`

`8t - (2)/(t) -15 = 0`

`(8t^2-2-15t)/(t)`
`= 0`

`8t^2 -15t -2 = 0`

`t(8t + 1) -2 (8t + 1) = 0`

`(8t + 1)(t-2) = 0`

`8t+1 = 0 ; t-2=0`

`t = -(1)/(8); t=2`

5. Substitute back:

`2^x =(1)/(8) ; 2^x = 2`

6. Solve for x

`2^x = -(1)/(8)` is false for any value of x because the exponential function is always positive, so there is no real solution.

`2^x = 2^1` since the bases are the same, set the exponents equal

x = 1