Final answer:
The student's question is about simplifying a log expression using properties of exponents and logarithms, such as the logarithm of a product and the rule of coefficients as exponents.
Step-by-step explanation:
The student's question involves simplifying a logarithmic expression using the properties of exponents and logarithms. The key properties used here are that the logarithm of a product is the sum of the logarithms, and the coefficient in front of the logarithm acts as an exponent inside the argument of the logarithm.
To simplify the given expression, we would use the following steps:
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- Apply the logarithm property that № – log_ab = log_a + log_b to combine the terms inside the parentheses.
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- Use the power rule of logarithms, which states that a coefficient in front of a logarithm can be moved inside the logarithm as an exponent: alog_b(x) = log_b(x^a).
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- Finally, apply these transformations step-by-step to the original expression to achieve the simplified result.
Therefore, the expression – (1)/(6)(log(6)x + log(6)y) – 2log(6)(x+3) can be simplified by first combining the logarithms and then applying the power rule to the – 2 coefficient in front of the second logarithm.