What is the answer to 2^{2x-3}=5^{x-2} ?

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

Solve for x: 2^{2x-3}=5^{x-2}

The solution is x=(2ln(5)-3ln(2))/(ln(5)-2ln(2))

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

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

Decimal

x = 5.10628 \dots

Solution steps

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

Apply exponent rules

(2 x - 3) ln (2) = (x - 2) ln (5)

Solve

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

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

1 0^{- x} = 169

- e^{x} x - 6 e^{x} = 0

3^{x + 1} = 4^{x}

3 6^{x - 5} = \frac{1}{6}

25 = \frac{100 ( 0.5 ) ^{t}}{5730}

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