What is the answer to 2^{x+2}-2^{x-3}=12 ?

The answer to 2^{x+2}-2^{x-3}=12 is x=(ln(12/31))/(ln(2))+3

Solve for x: 2^{x+2}-2^{x-3}=12

The solution is x=(ln(12/31))/(ln(2))+3

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2^{x + 2} - 2^{x - 3} = 12

x = \frac{ln ( \frac{12}{31} )}{ln ( 2 )} + 3

Solution steps

2^{x + 2} - 2^{x - 3} = 12

Factor

2^{x + 2} - 2^{x - 3} : 31 \cdot 2^{x - 3}

31 \cdot 2^{x - 3} = 12

Divide both sides by

31

2^{x - 3} = \frac{12}{31}

Apply exponent rules

(x - 3) ln (2) = ln (\frac{12}{31})

Solve

(x - 3) ln (2) = ln (\frac{12}{31}) : x = \frac{ln ( \frac{12}{31} )}{ln ( 2 )} + 3

x = \frac{ln ( \frac{12}{31} )}{ln ( 2 )} + 3

7^{3 - 2 x} = 7^{- x}

2^{x} - 2^{- x} = 5 - 5 \cdot 2^{- x}

3^{5 x} \cdot 9^{x^{2}} = 27

2700 = 860 (1.015)^{0.61 x} + 1000

1 0^{3 + x} = 810

What is the answer to 2^{x+2}-2^{x-3}=12 ?
The answer to 2^{x+2}-2^{x-3}=12 is x=(ln(12/31))/(ln(2))+3
Solve for x: 2^{x+2}-2^{x-3}=12
The solution is x=(ln(12/31))/(ln(2))+3