1.2 Solve simultaneously for x and \( \mathrm{y}: 2^{x} .4^{y}= \)

To solve the equation \( 2^x \cdot 4^y = 2^3 \) simultaneously, we can first rewrite \( 4^y \) in terms of base 2. Since \( 4 = 2^2 \), we have \( 4^y = (2^2)^y = 2^{2y} \). Therefore, we can rewrite the original equation as: \[ 2^x \cdot 2^{2y} = 2^3. \] Combining the exponents on the left side gives us: \[ 2^{x + 2y} = 2^3. \] This means we can set the exponents equal to each other: \[ x + 2y = 3. \] Now, we need another equation to solve for \( x \) and \( y \). Without more context or another equation, we can't find unique values for \( x \) and \( y \), but we can express one variable in terms of the other. For example, we could express \( x \) as: \[ x = 3 - 2y. \] This gives us a linear relationship between \( x \) and \( y \) that can be plotted or further analyzed for specific values of \( y \). If you have another equation or specific values, feel free to share!