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Example 1
If $log_3(9^a)=7$, then $a =$ ?
- $7$
- $14$
- $3\dfrac{1}{2}$
- $7\dfrac{1}{2}$
- $1$
Solution
- 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
$3^7=9^a$
- We now substitute $9$ by $3^2$ in the above equation
$3^7=(3^2)^a$
- Which may be written as
$3^7=3^{2a}$
- 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
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