https://file.aiquickdraw.com/mathbot/file/17259008328509iwxg0iw.jpg

The expression in the image can be interpreted as follows:

\[
2 \log 8 + 6 \log 3 - \log 12 - \log 5
\]

Let's simplify this expression step by step using logarithmic properties. We'll use the following logarithmic rules:

1. \(\log_a(x^n) = n \log_a x\)
2. \(\log_a x + \log_a y = \log_a (x \cdot y)\)
3. \(\log_a x - \log_a y = \log_a \left(\frac{x}{y}\right)\)

### Step 1: Apply the first property to the terms with coefficients

\[
2 \log 8 = \log (8^2) = \log 64
\]
\[
6 \log 3 = \log (3^6) = \log 729


Simplify the expression: 2 log 8 + 6 log 3 - log 12 - log 5.

Learn how to simplify the logarithmic expression 2 log 8 + 6 log 3 - log 12 - log 5 using key logarithmic properties. This step-by-step guide covers essential logarithmic formulas, including power, product, and quotient rules, suitable for high school students.

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