What is the answer to 5^{3x}*2^x=sqrt(250) ?

The answer to 5^{3x}*2^x=sqrt(250) is x=(ln(250))/(6ln(5)+2ln(2))

Solve for x: 5^{3x}*2^x=sqrt(250)

The solution is x=(ln(250))/(6ln(5)+2ln(2))

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5^{3 x} \cdot 2^{x} = 250

x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}

Decimal Notation

x = 0.5

Solution steps

5^{3 x} \cdot 2^{x} = 250

Apply exponent rules

(lo g_{2} (5) \cdot 3 x + x) ln (2) = \frac{1}{2} ln (250)

Solve

(lo g_{2} (5) \cdot 3 x + x) ln (2) = \frac{1}{2} ln (250) : x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}

x = \frac{ln ( 250 )}{6 ln ( 5 ) + 2 ln ( 2 )}

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

x, \frac{e ^{x}}{1 - x} = 0

2 \cdot 3^{2 x} = 72

3^{3 x} = 9 (3^{2 x})

2^{4 n} = 2^{5 n - 3}

What is the answer to 5^{3x}*2^x=sqrt(250) ?
The answer to 5^{3x}*2^x=sqrt(250) is x=(ln(250))/(6ln(5)+2ln(2))
Solve for x: 5^{3x}*2^x=sqrt(250)
The solution is x=(ln(250))/(6ln(5)+2ln(2))