Solve for a: Division of Logarithms with Base 7 and 9 Equation

The colon (:) represents division! So $A : B$ means $A ÷ B$. This notation is common in some countries but might look unfamiliar.

This comes from the change of base formula! When you have $\log_a b$ and $\log_b a$, they are reciprocals of each other. So $\log_9 7 \times \log_7 9 = 1$.

Because we're solving $a^2 = 4$! When you take the square root of both sides, you get two solutions: $a = +2$ and $a = -2$. Both work because $(+2)^2 = (-2)^2 = 4$.

Substitute back into the simplified equation! We found $4a^2 = 16$, so check: $4(±2)^2 = 4(4) = 16$ ✓. Both values work!

You can use the change of base formula: $\log_a b = \frac{\log b}{\log a}$. So $\log_9 7 = \frac{\log 7}{\log 9}$ and $\log_7 9 = \frac{\log 9}{\log 7}$ - notice they're reciprocals!