What is the answer to 2^{5x}=3^{2x+1} ?

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

Solve for x: 2^{5x}=3^{2x+1}

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

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

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

Decimal Notation

x = 0.86606 \dots

Solution steps

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

Apply exponent rules

5 x ln (2) = (2 x + 1) ln (3)

Solve

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

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

2^{x - 1} = 1

81 = 3^{x}

3^{2 x} = 27

2^{x} = x^{100}

lo g_{2} (16) = 8 \cdot 2^{- x}

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