Question

Suppose that ln 2 = a and ln 3 = b. Use properties of logarithms to write each logarithm in terms of a and b.

$\ln 27$

Short answer

The result is $3b$.

Step-by-step solution

Step 1. Given information.

Consider the given information.

$\ln 27$

Step 2. Calculation.

Apply the property ${\log }_a{M}^r=r{\log }_{a}M$.

$\begin{array}{rcl}\ln 27& =& \ln 3^3\\ & =& 3\ln 3\end{array}$

Step 3. Substitute the given values.

Substitute ln 2 = a and ln 3 = bin the obtained result.

$3\log 3=3b$