Solve the Logarithm Product: log₃7 × log₇9 Step-by-Step

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To solve the expression $\log_3 7 \times \log_7 9$, we use a known logarithmic property. This property states that:

$\log_a b \times \log_b c = \log_a c$

Applying this property allows us to simplify:

$\log_3 7 \times \log_7 9 = \log_3 9$

Next, we need to calculate $\log_3 9$. Since 9 can be expressed as $3^2$, we have:

$\log_3 9 = \log_3(3^2)$

Using the power rule of logarithms, $\log_b (x^n) = n \cdot \log_b x$, we find:

$\log_3(3^2) = 2 \cdot \log_3 3$

Since $\log_3 3 = 1$, it follows that:

$2 \cdot 1 = 2$

Therefore, the value of $\log_3 7 \times \log_7 9$ is $2$.

The correct answer choice is therefore Choice 3: $2$.