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

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

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

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

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

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

Decimal Notation

x = - 0.59057 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

7^{4} x + 1 = 5^{x}

2 = 2^{x}

4^{x} + 1 = 64

2^{4} \cdot 2^{3 n - 1} = 64

2^{a} = 4

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