Combine logarithms: We will use the property of logarithms that states ln(a) - ln(b) = ln(a/b). This allows us to combine the two logarithms into one. ln(8) - ln(4) = ln(8/4)Simplify fraction: Now we simplify the fraction 8/4. 8 divided by 4 equals 2. ln(8/4) = ln(2)Final answer: Since ln(2) cannot be simplified further without a calculator, we have reached our final answer. ln(2) is the natural logarithm of 2.

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$\ln (8) - \ln (4)$

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\ln (8) - \ln (4)

Combine logarithms: We will use the property of logarithms that states $\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right)$ . This allows us to combine the two logarithms into one. $\ln(8) - \ln(4) = \ln\left(\frac{8}{4}\right)$
Simplify fraction: Now we simplify the fraction $\frac{8}{4}$ . $8$ divided by $4$ equals $2$ . $\ln(\frac{8}{4}) = \ln(2)$
Final answer: Since $\ln(2)$ cannot be simplified further without a calculator, we have reached our final answer. $\newline$ $\ln(2)$ is the natural logarithm of $2$ .