What is the answer to 2/(3-2^x)=5 ?

The answer to 2/(3-2^x)=5 is x=(ln(13/5))/(ln(2))

Solve for x: 2/(3-2^x)=5

The solution is x=(ln(13/5))/(ln(2))

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\frac{2}{3 - 2 ^{x}} = 5

x = \frac{ln ( \frac{13}{5} )}{ln ( 2 )}

Decimal Notation

x = 1.37851 \dots

Solution steps

\frac{2}{3 - 2 ^{x}} = 5

Multiply both sides by

3 - 2^{x}

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

Simplify

2 = 5 (3 - 2^{x})

Switch sides

5 (3 - 2^{x}) = 2

Divide both sides by

5

3 - 2^{x} = \frac{2}{5}

Move

3

to the right side

- 2^{x} = - \frac{13}{5}

Divide both sides by

- 1

2^{x} = \frac{13}{5}

Apply exponent rules

x ln (2) = ln (\frac{13}{5})

Solve

x ln (2) = ln (\frac{13}{5}) : x = \frac{ln ( \frac{13}{5} )}{ln ( 2 )}

x = \frac{ln ( \frac{13}{5} )}{ln ( 2 )}

Verify Solutions:

x = \frac{ln ( \frac{13}{5} )}{ln ( 2 )}

True

The solution is

x = \frac{ln ( \frac{13}{5} )}{ln ( 2 )}

2 e^{2 x} = e^{x + 1}

a, f (a + 2) = 2^{(a + 2)}

5^{x + 1} + 6 \cdot 5^{x} = 6

2^{2 x} = 31

1.0 6^{x} = 4.1

What is the answer to 2/(3-2^x)=5 ?
The answer to 2/(3-2^x)=5 is x=(ln(13/5))/(ln(2))
Solve for x: 2/(3-2^x)=5
The solution is x=(ln(13/5))/(ln(2))