What is the answer to 3^{6x}=13^{x-3} ?

The answer to 3^{6x}=13^{x-3} is x=-(3ln(13))/(6ln(3)-ln(13))

Solve for x: 3^{6x}=13^{x-3}

The solution is x=-(3ln(13))/(6ln(3)-ln(13))

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3^{6 x} = 1 3^{x - 3}

x = - \frac{3 ln ( 13 )}{6 ln ( 3 ) - ln ( 13 )}

Decimal Notation

x = - 1.91094 \dots

Solution steps

3^{6 x} = 1 3^{x - 3}

Apply exponent rules

6 x ln (3) = (x - 3) ln (13)

Solve

6 x ln (3) = (x - 3) ln (13) : x = - \frac{3 ln ( 13 )}{6 ln ( 3 ) - ln ( 13 )}

x = - \frac{3 ln ( 13 )}{6 ln ( 3 ) - ln ( 13 )}

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

5 = e^{x}

e^{x} - 5 = 3

e^{x} - 4 = 0

2^{2 x} - 9 \cdot 2^{x} + 8 = 0

What is the answer to 3^{6x}=13^{x-3} ?
The answer to 3^{6x}=13^{x-3} is x=-(3ln(13))/(6ln(3)-ln(13))
Solve for x: 3^{6x}=13^{x-3}
The solution is x=-(3ln(13))/(6ln(3)-ln(13))