What is the answer to 5^{x-1}=13^{3x} ?

The answer to 5^{x-1}=13^{3x} is x=(ln(5))/(ln(5)-3ln(13))

Solve for x: 5^{x-1}=13^{3x}

The solution is x=(ln(5))/(ln(5)-3ln(13))

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

x = \frac{ln ( 5 )}{ln ( 5 ) - 3 ln ( 13 )}

Decimal Notation

x = - 0.26447 \dots

Solution steps

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

Apply exponent rules

(x - 1) ln (5) = 3 x ln (13)

Solve

(x - 1) ln (5) = 3 x ln (13) : x = \frac{ln ( 5 )}{ln ( 5 ) - 3 ln ( 13 )}

x = \frac{ln ( 5 )}{ln ( 5 ) - 3 ln ( 13 )}

5000000 = 1000000 e^{0.645 t}

6^{x} = 5 \cdot 3^{x + 1}

2^{x} = 3^{(x - 1)}

\frac{1}{3} = 3^{(2 x + 2)}

What is the answer to 5^{x-1}=13^{3x} ?
The answer to 5^{x-1}=13^{3x} is x=(ln(5))/(ln(5)-3ln(13))
Solve for x: 5^{x-1}=13^{3x}
The solution is x=(ln(5))/(ln(5)-3ln(13))