CMA Foundation · Fundamentals of Business Mathematics and Statistics · Indices and Logarithms
What is the value of log 25 + log 4 - log 1000 + log 10 (all to base 10)?
The value is 0. Combining the terms with the product and quotient laws gives the logarithm of (25 times 4 times 10) divided by 1000, which is log of 1000/1000 equals log 1, and the logarithm of 1 is zero.
- A0Correct
- B1
- C-1
- D2
Explanation
log 25 + log 4 = log 100 = 2. Then 2 - log 1000 = 2 - 3 = -1. Adding log 10 = 1 gives -1 + 1 = 0. Check by combining: (25 x 4 x 10)/1000 = 1, and log 1 = 0. Choosing 1 results from forgetting to subtract fully, and 2 from ignoring the last two terms.
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