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

The answer to 2^{x+6}-2^{x+2}=1 is x=-(ln(15))/(ln(2))-2

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

The solution is x=-(ln(15))/(ln(2))-2

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

x = - \frac{ln ( 15 )}{ln ( 2 )} - 2

Decimal Notation

x = - 5.90689 \dots

Solution steps

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

Factor

2^{x + 6} - 2^{x + 2} : 15 \cdot 2^{x + 2}

15 \cdot 2^{x + 2} = 1

Divide both sides by

15

2^{x + 2} = \frac{1}{15}

Apply exponent rules

(x + 2) ln (2) = ln (\frac{1}{15})

Solve

(x + 2) ln (2) = ln (\frac{1}{15}) : x = - \frac{ln ( 15 )}{ln ( 2 )} - 2

x = - \frac{ln ( 15 )}{ln ( 2 )} - 2

x^{x} = e

51 e^{3 x} = 102

9^{x} = 3^{x + 5}

ln (e^{3 + 2 l n (x)}) = 58

3^{- x} = 27

What is the answer to 2^{x+6}-2^{x+2}=1 ?
The answer to 2^{x+6}-2^{x+2}=1 is x=-(ln(15))/(ln(2))-2
Solve for x: 2^{x+6}-2^{x+2}=1
The solution is x=-(ln(15))/(ln(2))-2