Question

Rewrite the expression  log3z+log32+log34 as a single logarithm.(1 point)Responseslog3(24z)logarithm subscript 3 baseline left parenthesis 24 z right parenthesislog3(z+6)logarithm subscript 3 baseline left parenthesis z plus 6 right parenthesislog3(8z)logarithm subscript 3 baseline left parenthesis 8 z right parenthesislog3(6z)

Answer 1

To combine the expression \( \log_3 z + \log_3 2 + \log_3 4 \) into a single logarithm, we can use the properties of logarithms, specifically:

1. \( \log_b a + \log_b c = \log_b (a \cdot c) \)

Let's apply this property step by step:

1. Combine \( \log_3 z \) and \( \log_3 2 \):

\[ \log_3 z + \log_3 2 = \log_3 (z \cdot 2) = \log_3 (2z) \]

2. Now combine \( \log_3 (2z) \) and \( \log_3 4 \):

\[ \log_3 (2z) + \log_3 4 = \log_3 ((2z) \cdot 4) = \log_3 (8z) \]

So, the expression \( \log_3 z + \log_3 2 + \log_3 4 \) can be rewritten as:

\[ \log_3 (8z) \]

Thus, the final answer is:

\[ \log_3(8z) \]