A telecom analyst multiplies tower count, traffic share, and a growth ratio, all positive, and the product overflows the worksheet. The analyst takes a logarithm of that product. What does that step do to the calculation?
Select an answer to reveal the explanation.
Short Explanation
A logarithm turns a tower of multiplications into a stack of additions you can finish. You replace the product of those positive factors with the sum of their logs. The trap is thinking the log merely averages the factors or squeezes them into a ratio.
Full Explanation
For positive numbers, the log of a product equals the sum of the logs. Taking the logarithm of tower count times traffic share times the growth ratio replaces that product with the sum of their logs, which the worksheet can add without multiplying the original factors together. The overflow came from the product; the sum of logs is a different calculation with the same ordering information once the base is fixed. Rewriting the product as a ratio of the largest factor to the smallest throws away a factor and is not a logarithm. The arithmetic mean adds the factors and divides; it is not the log of their product and does not preserve the combined scale. Raising the product to another power makes the number larger or smaller as a power, and it is not the identity that turns a product into a sum. Exam caveat: the identity needs factors in the domain of the log, which these positive factors are; the log of a sum is not the sum of logs. Operational check: confirm the sheet adds the logs of the factors, or exponentiates that sum, rather than multiplying the raw factors in the overflowing cell.