Questions: Solve for (x) and (y) in the given expressions. Express these answers to the tenths place (i.e., one digit after the decimal point). [ 0.42=log (x) 0.42=ln (y) ]

Solution Steps

To solve for \( x \) and \( y \) in the given expressions, we need to use the properties of logarithms and exponentials. Specifically, we will use the fact that \( \log(x) = a \) implies \( x = 10^a \) and \( \ln(y) = b \) implies \( y = e^b \).

Given the equation: \[ 0.42 = \log(x) \] We use the property of logarithms that states \( \log(x) = a \) implies \( x = 10^a \). Therefore: \[ x = 10^{0.42} \]

Given the equation: \[ 0.42 = \ln(y) \] We use the property of natural logarithms that states \( \ln(y) = b \) implies \( y = e^b \). Therefore: \[ y = e^{0.42} \]

Using the properties from the previous steps, we calculate: \[ x = 10^{0.42} \approx 2.6303 \] \[ y = e^{0.42} \approx 1.5210 \]

Rounding the values to one digit after the decimal point: \[ x \approx 2.6 \] \[ y \approx 1.5 \]

Final Answer