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

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

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

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

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

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

Decimal Notation

x = 16.68478 \dots

Solution steps

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

Apply exponent rules

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

Solve

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

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

10 e^{2 n - 10} - 5 = 73

e^{e^{x}} = 3

4 9^{x} = \frac{1}{7}

27 = (\frac{1}{3})^{x}

3^{2 x} = 9^{3 x - 4}

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