What is the answer to 2^{x-1}+1/(2^{x-3)}=5 ?

The answer to 2^{x-1}+1/(2^{x-3)}=5 is x=3,x=1

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2^{x-1}+1/(2^{x-3)}=5

2^{x - 1} + \frac{1}{2 ^{x - 3}} = 5

x = 3, x = 1

Solution steps

2^{x - 1} + \frac{1}{2 ^{x - 3}} = 5

Apply exponent rules

2^{x} \cdot 2^{- 1} + (2^{x})^{- 1} \cdot 2^{3} = 5

Rewrite the equation with

2^{x} = u

u \cdot 2^{- 1} + (u)^{- 1} \cdot 2^{3} = 5

Solve

u \cdot 2^{- 1} + u^{- 1} \cdot 2^{3} = 5 : u = 8, u = 2

u = 8, u = 2

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

Solve

2^{x} = 2 : x = 1

x = 3, x = 1

Verify Solutions:

x = 3

True

, x = 1

True

The solutions are

x = 3, x = 1

7 \cdot e^{0.1 t} = 47

e^{7 - 4 x} = 5

2^{2 x} - 12 \cdot 2^{x} + 32 = 0

1 0^{5 + 8 x} = 79800

3 \cdot 2 0^{x} = 2^{x + 1}

What is the answer to 2^{x-1}+1/(2^{x-3)}=5 ?
The answer to 2^{x-1}+1/(2^{x-3)}=5 is x=3,x=1
Solve for x: 2^{x-1}+1/(2^{x-3)}=5
The solution is x=3,x=1