Math

Question Round log742\log_{7} 42 to the nearest thousand.

Studdy Solution

STEP 1

Assumptions
1. We are given that log7421.92\log _{7} 42 \approx 1.92.
2. We are asked to round this approximation to the nearest thousandth.

STEP 2

To round the given logarithm to the nearest thousandth, we need to look at the fourth decimal place.

STEP 3

Since the given approximation is log7421.92\log _{7} 42 \approx 1.92, we assume the third decimal place is zero, as it is not provided. Thus, we consider the number as 1.9201.920.

STEP 4

The fourth decimal place is not given, so we assume it is less than 5 because if it were 5 or more, it would have been rounded up and affected the third decimal place.

STEP 5

Since the fourth decimal place is assumed to be less than 5, we do not need to increase the third decimal place when rounding to the nearest thousandth.

STEP 6

Therefore, the logarithm rounded to the nearest thousandth is 1.9201.920.
log7421.920\log _{7} 42 \approx 1.920 when rounded to the nearest thousandth.

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