What is the answer to 2^{x-1}+2^x-5=2^{x-2}+6 ?

The answer to 2^{x-1}+2^x-5=2^{x-2}+6 is x=(ln(11/5))/(ln(2))+2

Solve for x: 2^{x-1}+2^x-5=2^{x-2}+6

The solution is x=(ln(11/5))/(ln(2))+2

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2^{x - 1} + 2^{x} - 5 = 2^{x - 2} + 6

x = \frac{ln ( \frac{11}{5} )}{ln ( 2 )} + 2

Solution steps

2^{x - 1} + 2^{x} - 5 = 2^{x - 2} + 6

Subtract

2^{x - 2}

from both sides

2^{x - 1} + 2^{x} - 5 - 2^{x - 2} = 2^{x - 2} + 6 - 2^{x - 2}

Simplify

2^{x - 1} + 2^{x} - 5 - 2^{x - 2} = 6

Factor

2^{x - 1} + 2^{x} - 5 - 2^{x - 2} : 5 (2^{x - 2} - 1)

5 (2^{x - 2} - 1) = 6

Divide both sides by

5

2^{x - 2} - 1 = \frac{6}{5}

Move

1

to the right side

2^{x - 2} = \frac{11}{5}

Apply exponent rules

(x - 2) ln (2) = ln (\frac{11}{5})

Solve

(x - 2) ln (2) = ln (\frac{11}{5}) : x = \frac{ln ( \frac{11}{5} )}{ln ( 2 )} + 2

x = \frac{ln ( \frac{11}{5} )}{ln ( 2 )} + 2

x = 3 e^{2 x}

4^{- (x - 4)} = \frac{1}{16}

a = 30 \cdot 5^{0.078 x}

3^{x + 2} - 10 \cdot 3^{x} + 9 = 0

9 e^{5 x} = 100

What is the answer to 2^{x-1}+2^x-5=2^{x-2}+6 ?
The answer to 2^{x-1}+2^x-5=2^{x-2}+6 is x=(ln(11/5))/(ln(2))+2
Solve for x: 2^{x-1}+2^x-5=2^{x-2}+6
The solution is x=(ln(11/5))/(ln(2))+2