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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