Question

question 1329
13 which of the following would be equivalent to log 30?
a ( log 60 + log 2 )
b ( log 27 + log 3 )
c ( log 6 cdot log 5 )
d ( log 15 + log 2 )

Explanation:

Step1: Recall Logarithm Product Rule

The logarithm product rule states that \(\log a + \log b=\log(ab)\) for \(a,b>0\). We will apply this rule to each option.

Step2: Analyze Option A

For option A: \(\log 60+\log 2\). Using the product rule, \(\log 60+\log 2 = \log(60\times2)=\log(120)
eq\log(30)\).

Step3: Analyze Option B

For option B: \(\log 27+\log 3\). Using the product rule, \(\log 27+\log 3=\log(27\times3)=\log(81)
eq\log(30)\).

Step4: Analyze Option C

For option C: \(\log 6\cdot\log 5\). The product rule is for addition of logs, not multiplication. So this is not equivalent to \(\log(30)\) (since \(\log a\cdot\log b
eq\log(ab)\) in general).

Step5: Analyze Option D

For option D: \(\log 15+\log 2\). Using the product rule, \(\log 15+\log 2=\log(15\times2)=\log(30)\), which matches the given \(\log(30)\).

Answer:

D. \(\log 15 + \log 2\)