Questions: Use the References to access important values if needed for this question. Two-Step Algebra ln a = -bc + ln d In order to solve the equation above for c, you must: Step One Add the same expression to each side of the equation to leave the term that includes the variable by itself on the right-hand side of the expression: +ln a = -bc + ln d

Solution Steps

To solve the given equation \(\ln a = -bc + \ln d\) for \(c\), we need to isolate \(c\) on one side of the equation. Here are the high-level steps:

1. Subtract \(\ln d\) from both sides to isolate the term involving \(c\).
2. Divide both sides by \(-b\) to solve for \(c\).

Given the equation: \[ \ln a = -bc + \ln d \] Subtract \(\ln d\) from both sides: \[ \ln a - \ln d = -bc \]

Using the properties of logarithms, \(\ln a - \ln d\) can be simplified to \(\ln \left(\frac{a}{d}\right)\): \[ \ln \left(\frac{a}{d}\right) = -bc \]

Divide both sides by \(-b\): \[ c = -\frac{\ln \left(\frac{a}{d}\right)}{b} \]

Substitute \(a = 5\), \(d = 3\), and \(b = 2\) into the equation: \[ c = -\frac{\ln \left(\frac{5}{3}\right)}{2} \]

Calculate \(\ln \left(\frac{5}{3}\right)\): \[ \ln \left(\frac{5}{3}\right) \approx 0.5108 \] Then: \[ c = -\frac{0.5108}{2} \approx -0.2554 \]

Final Answer