Example Question 2

Example corresponding to question 2 in college algebra 1.

Example 1


Express as a single logarithm: $3\log_b x+2\log_b y - \dfrac{1}{3}\log_b z$

  1. $\log_b \dfrac{x^3 \cdot y^2}{\sqrt[3]z}$


  2. $\log_b \dfrac{x^3 \cdot y^2}{\dfrac{1}{3}z}$


  3. $\dfrac{1}{3}\log_b \dfrac{x^3 \cdot y^2}{z}$


  4. $\log_b 18\dfrac{x \cdot y}{z}$


  5. $\log_b \dfrac{x \cdot y}{z}$

Solution


  1. We first use the power formula $n\log_b x = \log_b x^n$ to write the given expression as follows
    $3\log_b x+2\log_b y - \dfrac{1}{3}\log_b z = \log_b x^3+\log_b y^2 - \log_b z^{\tfrac{1}{3}}$

  2. We now use the formula $\log_b A + \log_b B = \log_b A \cdot B$ to write the above expression as follows

    $=\log_b (x^3 \cdot y^2)-\log_b z^{\tfrac{1}{3}}$


  3. We now use the formula $\log_b A - \log_b B = \log_b \dfrac{A}{B}$ to rewrite the above expression as follows

    $=\log_b \dfrac{x^3 \cdot y^2}{z^{\tfrac{1}{3}}}=\log_b \dfrac{x^3 \cdot y^2}{\sqrt[3]z}$



    Answer A