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

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

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

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

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

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

Decimal Notation

x = 21.63770 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

5^{(x)} + 5^{(5 - x)} = 150

e^{- x} = - x

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

2^{5 x} = 128

e^{x^{2}} = \frac{1}{9}

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