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

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

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

x = 3

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

2^{x} = u

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

Solve

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

u = 8

Substitute back

u = 2^{x},

solve for

x

Solve

2^{x} = 8 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

2^{x} = 3^{x}

8 (3^{x}) + 5 (2^{x}) - 6^{x} = 40

2^{x} = x^{2}

e^{x} = 2

3 \cdot 2^{x} = (\frac{1}{3}) \cdot 4^{x}

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
Solve for x: (2^{x-1}+1)/((2^{x-3))}=5
The solution is x=3