Chapter 5.5, Problem 34AYU

To determine

Use properties of logarithm to write each logarithm in terms of $a$ and $b$ .

Answer to Problem 34AYU

  $\boxed{\ln 27=3b}$

Explanation of Solution

Given information:

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

  $\ln 27$

Calculation:

Consider the given expression,

  $\ln 27$

  $\ln 27=\ln 3^3$

Apply logarithm property $M=Nthen{\log }_{a}M={\log }_{a}N$ (base can $10$ or $a$ )

  $\ln 27=3\ln 3\left[\therefore {\log }_a{M}^r=r{\log }_{a}M\right]$

Substitute $a$ for $2$ and $b$ for $3$ .

  $\ln 27=3b$

Hence, $\boxed{\ln 27=3b}$