What is the answer to 5^{3x+1}=4^{x-5} ?

The answer to 5^{3x+1}=4^{x-5} is x=-(ln(5120))/(3ln(5)-2ln(2))

Solve for x: 5^{3x+1}=4^{x-5}

The solution is x=-(ln(5120))/(3ln(5)-2ln(2))

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5^{3 x + 1} = 4^{x - 5}

x = - \frac{ln ( 5120 )}{3 ln ( 5 ) - 2 ln ( 2 )}

Decimal Notation

x = - 2.48136 \dots

Solution steps

5^{3 x + 1} = 4^{x - 5}

Apply exponent rules

(3 x + 1) ln (5) = (x - 5) ln (4)

Solve

(3 x + 1) ln (5) = (x - 5) ln (4) : x = - \frac{ln ( 5120 )}{3 ln ( 5 ) - 2 ln ( 2 )}

x = - \frac{ln ( 5120 )}{3 ln ( 5 ) - 2 ln ( 2 )}

3^{2 - x} = 400

2^{x^{2} + 2 x} = 8

5^{x} = 83

1 6^{r} \cdot 6 4^{3 - 3 r} = 64

y, 2^{2 y + 1} = x

What is the answer to 5^{3x+1}=4^{x-5} ?
The answer to 5^{3x+1}=4^{x-5} is x=-(ln(5120))/(3ln(5)-2ln(2))
Solve for x: 5^{3x+1}=4^{x-5}
The solution is x=-(ln(5120))/(3ln(5)-2ln(2))