What is the answer to 2^{x-1}-2^{x-3}=3^{x-2}-3^{x-3} ?

The answer to 2^{x-1}-2^{x-3}=3^{x-2}-3^{x-3} is x=(4ln(3)-4ln(2))/(ln(3)-ln(2))

Solve for x: 2^{x-1}-2^{x-3}=3^{x-2}-3^{x-3}

The solution is x=(4ln(3)-4ln(2))/(ln(3)-ln(2))

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2^{x - 1} - 2^{x - 3} = 3^{x - 2} - 3^{x - 3}

x = \frac{4 ln ( 3 ) - 4 ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

Decimal Notation

x = 4

Solution steps

2^{x - 1} - 2^{x - 3} = 3^{x - 2} - 3^{x - 3}

Simplify

2^{x - 1} - 2^{x - 3} : 3 \cdot 2^{x - 3}

Simplify

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

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

Apply exponent rules

ln (3) + (x - 3) ln (2) = ln (2) + (x - 3) ln (3)

Solve

ln (3) + (x - 3) ln (2) = ln (2) + (x - 3) ln (3) : x = \frac{4 ln ( 3 ) - 4 ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

x = \frac{4 ln ( 3 ) - 4 ln ( 2 )}{ln ( 3 ) - ln ( 2 )}

2^{x + 1} + 2^{3 - x} = 17

2^{5 x} = 94

\frac{1}{8} = 8^{x}

e^{x} - 5 e^{- x} = 4

3 6^{- 3} = 21 6^{2 x + 2}

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