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

Solve the following equation.Please help with this question and show working-example-1
User Buchi
by
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1 Answer

3 votes

Answer:

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

User EggMeister
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