What is the answer to 20^{-2x+3}=4^{3x-1}*5^{-x+4} ?

The answer to 20^{-2x+3}=4^{3x-1}*5^{-x+4} is x=(2ln(2)-ln(5/64))/(2ln(20)+6ln(2)-ln(5))

Solve for x: 20^{-2x+3}=4^{3x-1}*5^{-x+4}

The solution is x=(2ln(2)-ln(5/64))/(2ln(20)+6ln(2)-ln(5))

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2 0^{- 2 x + 3} = 4^{3 x - 1} \cdot 5^{- x + 4}

x = \frac{2 ln ( 2 ) - ln ( \frac{5}{64} )}{2 ln ( 20 ) + 6 ln ( 2 ) - ln ( 5 )}

Decimal Notation

x = 0.46081 \dots

Solution steps

2 0^{- 2 x + 3} = 4^{3 x - 1} \cdot 5^{- x + 4}

Apply exponent rules

(- 2 x + 3) ln (20) = (3 x - 1 + lo g_{4} (5) (- x + 4)) ln (4)

Solve

(- 2 x + 3) ln (20) = (3 x - 1 + lo g_{4} (5) (- x + 4)) ln (4) : x = \frac{2 ln ( 2 ) - ln ( \frac{5}{64} )}{2 ln ( 20 ) + 6 ln ( 2 ) - ln ( 5 )}

x = \frac{2 ln ( 2 ) - ln ( \frac{5}{64} )}{2 ln ( 20 ) + 6 ln ( 2 ) - ln ( 5 )}

2^{x - 4} = 3 2^{x + 4}

5^{- x + 2} = 1 1^{7 x}

3^{- 2 x + 1} \cdot 3^{- 2 x - 3} = 3^{- x}

e^{x} + \frac{1}{2} = 0

2^{x - 2} = 64

What is the answer to 20^{-2x+3}=4^{3x-1}*5^{-x+4} ?
The answer to 20^{-2x+3}=4^{3x-1}*5^{-x+4} is x=(2ln(2)-ln(5/64))/(2ln(20)+6ln(2)-ln(5))
Solve for x: 20^{-2x+3}=4^{3x-1}*5^{-x+4}
The solution is x=(2ln(2)-ln(5/64))/(2ln(20)+6ln(2)-ln(5))