`2(log_3(20)-log_3(4))+0.5log_3(4)` Condense the expression.

`2(log_3 (20) - log_3 (4)) + 0.5log_3(4)`

First, apply the difference-quotient rule of logarithm `log_b (m/n) = log_b(m) - log_b(n)` .

`= 2 (log_3 (20/4))+0.5log_3(4)`

`=2log_3(5) + 0.5log_3(4)`

Then, apply the power rule `log_b(a^m) = m*log_b(a)` .

`= log_3(5^2) + log_3(4^0.5)`

`=log_3(25) + log_3(2)`

And, apply the sum-product rule `log_b(m*n) = log_b(m) + log_b(n)` .

`= log_3(25*2)`

`=log_3(50)`

Therefore, `2(log_3 (20) - log_3 (4)) + 0.5log_3(4)=log_3(50)` .

Comments

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