What is the answer to solvefor x,2^x*3^y=12 ?

The answer to solvefor x,2^x*3^y=12 is x=(2ln(2)+ln(3)(-y+1))/(ln(2))

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solvefor x,2^x*3^y=12

solve for

x, 2^{x} \cdot 3^{y} = 12

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

Solution steps

2^{x} \cdot 3^{y} = 12

Divide both sides by

3^{y}

2^{x} = \frac{12}{3 ^{y}}

Simplify

\frac{12}{3 ^{y}} : 4 \cdot 3^{1 - y}

2^{x} = 4 \cdot 3^{1 - y}

Apply exponent rules

x ln (2) = ln (4 \cdot 3^{1 - y})

Solve

x ln (2) = ln (4 \cdot 3^{1 - y}) : x = \frac{2 ln ( 2 ) + ln ( 3 ) ( - y + 1 )}{ln ( 2 )}

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

6^{n + 7} = 67

1 2^{5 x} = 3 \cdot 1 5^{3 x}

3^{x - 3} = 1 7^{- 5 x}

9 e^{x} = 3

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

What is the answer to solvefor x,2^x*3^y=12 ?
The answer to solvefor x,2^x*3^y=12 is x=(2ln(2)+ln(3)(-y+1))/(ln(2))