What is the answer to 5/(2*2^x-2^x-2^{-1)}=16 ?

The answer to 5/(2*2^x-2^x-2^{-1)}=16 is x=(ln(13/16))/(ln(2))

Solve for x: 5/(2*2^x-2^x-2^{-1)}=16

The solution is x=(ln(13/16))/(ln(2))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{5}{2 \cdot 2 ^{x} - 2 ^{x} - 2 ^{- 1}} = 16

x = \frac{ln ( \frac{13}{16} )}{ln ( 2 )}

Decimal Notation

x = - 0.29956 \dots

Solution steps

\frac{5}{2 \cdot 2 ^{x} - 2 ^{x} - 2 ^{- 1}} = 16

Multiply both sides by

2^{x} - 2^{- 1}

\frac{5}{2 \cdot 2 ^{x} - 2 ^{x} - 2 ^{- 1}} (2^{x} - 2^{- 1}) = 16 (2^{x} - 2^{- 1})

Simplify

\frac{5}{2 2 ^{x} - 2 ^{x} - 2 ^{- 1}} (2^{x} - 2^{- 1}) : 5

Simplify

16 (2^{x} - 2^{- 1}) : 16 (2^{x} - \frac{1}{2})

5 = 16 (2^{x} - \frac{1}{2})

Switch sides

16 (2^{x} - \frac{1}{2}) = 5

Divide both sides by

16

2^{x} - \frac{1}{2} = \frac{5}{16}

Move

\frac{1}{2}

to the right side

2^{x} = \frac{13}{16}

Apply exponent rules

x ln (2) = ln (\frac{13}{16})

Solve

x ln (2) = ln (\frac{13}{16}) : x = \frac{ln ( \frac{13}{16} )}{ln ( 2 )}

x = \frac{ln ( \frac{13}{16} )}{ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{13}{16} )}{ln ( 2 )}

True

The solution is

x = \frac{ln ( \frac{13}{16} )}{ln ( 2 )}

1 1^{9 x} = 4^{- x + 7}

7^{x} - 2^{x} = 0

2^{x} = n

x, 8^{2 x} - 4 (8^{x}) = 3 g

9^{x + 1} + 1 = 10 (3^{x})

What is the answer to 5/(2*2^x-2^x-2^{-1)}=16 ?
The answer to 5/(2*2^x-2^x-2^{-1)}=16 is x=(ln(13/16))/(ln(2))
Solve for x: 5/(2*2^x-2^x-2^{-1)}=16
The solution is x=(ln(13/16))/(ln(2))