Example Question 3

Example corresponding to question 3 in college algebra 2.

Example 1


If $log_3(9^a)=7$, then $a =$ ?

  1. $7$


  2. $14$


  3. $3\dfrac{1}{2}$


  4. $7\dfrac{1}{2}$


  5. $1$

Solution


  1. We first use the relationship between logarithmic and exponential function " $log_a(x)=y$ if and only if $a^y=x$ " to rewrite the given equation as follows

    $3^7=9^a$

  2. We now substitute $9$ by $3^2$ in the above equation

    $3^7=(3^2)^a$

  3. Which may be written as

    $3^7=3^{2a}$

  4. The left and right terms in the above equations are exponentials expressions to the same base, hence

    $7=2a$

    $a = \dfrac{7}{2} = 3\dfrac{1}{2}$

    Answer C