What is the answer to 2^{x-5}=5^{2x+6} ?

The answer to 2^{x-5}=5^{2x+6} is x=(6ln(5)+5ln(2))/(ln(2)-2ln(5))

Solve for x: 2^{x-5}=5^{2x+6}

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

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2^{x - 5} = 5^{2 x + 6}

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

Decimal Notation

x = - 5.19547 \dots

Solution steps

2^{x - 5} = 5^{2 x + 6}

Apply exponent rules

(x - 5) ln (2) = (2 x + 6) ln (5)

Solve

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

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

3^{x + 2} + 3^{x + 1} = 108

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

\frac{2 7 ^{3} 9 ^{- 2}}{81} = 3^{x}

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

8^{2 x + 1} = 12 8^{x - 3}

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