Simplifying the Expression 3log28 + 4log212 − log32 | Logarithmic Properties and Simplification Steps

Which is equivalent to 3log28 + 4log212 − log32?

To simplify the expression 3log28 + 4log212 − log32, we can use the properties of logarithms

To simplify the expression 3log28 + 4log212 − log32, we can use the properties of logarithms. The two properties we will use are:

1. Logarithmic identity: log_b(x^a) = a*log_b(x)

2. Logarithmic addition/subtraction: log_b(x) + log_b(y) = log_b(xy)

Applying these properties, we can simplify the given expression step by step:

1. 3log28 + 4log212 − log32

2. Applying property 1 to each logarithm:

= log28^3 + log212^4 − log32

3. Simplifying the exponents:

= log2184 + log248 − log32

4. Applying property 2 to add the logarithms:

= log2184 * 48 / 32

5. Simplifying further:

= log2272 / 32

6. Calculating the values:

= log2272 – log232

7. Simplifying:

= log232

Therefore, 3log28 + 4log212 − log32 is equivalent to log232.

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