What is the answer to 2^{(2x+3)}=3^{3x} ?

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

Solve for x: 2^{(2x+3)}=3^{3x}

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

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

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

Decimal Notation

x = 1.08897 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

5^{x} = 3125

3^{2 x + 1} - 10 (3^{x}) + 3 = 0

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

3^{x} = - 2

3^{x} = 21

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