What is the answer to 2^{5x+1}=81^{x-2} ?

The answer to 2^{5x+1}=81^{x-2} is x=(8ln(3)+ln(2))/(4ln(3)-5ln(2))

Solve for x: 2^{5x+1}=81^{x-2}

The solution is x=(8ln(3)+ln(2))/(4ln(3)-5ln(2))

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2^{5 x + 1} = 8 1^{x - 2}

x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}

Solution steps

2^{5 x + 1} = 8 1^{x - 2}

Apply exponent rules

(5 x + 1) ln (2) = (x - 2) ln (81)

Solve

(5 x + 1) ln (2) = (x - 2) ln (81) : x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}

x = \frac{8 ln ( 3 ) + ln ( 2 )}{4 ln ( 3 ) - 5 ln ( 2 )}

5^{x^{2} - 5 x + 6} = 1

5^{x + 1} = 5^{2 x - 3}

2^{1 - x} = 3

3^{x} = 11

y, x = 2^{y}

What is the answer to 2^{5x+1}=81^{x-2} ?
The answer to 2^{5x+1}=81^{x-2} is x=(8ln(3)+ln(2))/(4ln(3)-5ln(2))
Solve for x: 2^{5x+1}=81^{x-2}
The solution is x=(8ln(3)+ln(2))/(4ln(3)-5ln(2))