What is the answer to 7^{-x+2}=15^{-2x} ?

The answer to 7^{-x+2}=15^{-2x} is x=-(2ln(7))/(-ln(7)+2ln(15))

Solve for x: 7^{-x+2}=15^{-2x}

The solution is x=-(2ln(7))/(-ln(7)+2ln(15))

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

x = - \frac{2 ln ( 7 )}{- ln ( 7 ) + 2 ln ( 15 )}

Decimal Notation

x = - 1.12150 \dots

Solution steps

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

Apply exponent rules

(- x + 2) ln (7) = - 2 x ln (15)

Solve

(- x + 2) ln (7) = - 2 x ln (15) : x = - \frac{2 ln ( 7 )}{- ln ( 7 ) + 2 ln ( 15 )}

x = - \frac{2 ln ( 7 )}{- ln ( 7 ) + 2 ln ( 15 )}

2 x e^{x} - 3 e^{x} = 0

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

3 \cdot 4^{x} = 2 \cdot 1 2^{x}

2^{(- 3 x)} \cdot 4^{(2 x - 2)} = 16

2^{2 x} = 2^{x} + 12

What is the answer to 7^{-x+2}=15^{-2x} ?
The answer to 7^{-x+2}=15^{-2x} is x=-(2ln(7))/(-ln(7)+2ln(15))
Solve for x: 7^{-x+2}=15^{-2x}
The solution is x=-(2ln(7))/(-ln(7)+2ln(15))