Question

Log(3)8-log(3)4+log(3)9/2​

Answer 1

$log_{3}(8) - log_{3}(4) + log_{3}( \frac{9}{2} ) = log_{3}( \frac{8}{4} ) + log_{3}( \frac{9}{2} ) = \\ = log_{3}( \frac{8}{4} \times \frac{9}{2} ) = log_{3}(9) = log_{3}( {3}^{2} ) = 2$

Ответ: 2

Answer 2

To simplify the given expression, we can use the properties of logarithms:

1. Logarithmic Identity: log_b(a) - log_b(c) = log_b(a/c)
2. Logarithmic Power Rule: log_b(a^n) = n * log_b(a)

Let's apply these properties step by step:

Given expression: log(3)8 - log(3)4 + log(3)(9/2)

Apply the logarithmic identity to the first two terms: log(3)(8/4) + log(3)(9/2)

Simplify the fractions within the logarithms: log(3)2 + log(3)(9/2)

Now, apply the logarithmic power rule to the second term: log(3)2 + (log(3)9 - log(3)2)

Simplify the logarithmic terms: log(3)2 + (2*log(3)3 - log(3)2)

Since log(3)2 is common in both terms, combine them: 2*log(3)3

So, the simplified expression is: 2*log(3)3