Common Logarithms (Base 10)

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Show your work for each problem.

1.
What is $\log 10\,000$ ?
1. a)1000
2. b)10000
3. c)3
4. d)4
2.
What is $\log 1\,000\,000$ ?
3.
What is $\log 0.01$ ?
1. a)-2
2. b)2
3. c)0.01
4. d)-0.01
4.
What is $\log 1$ ?
5.
Find $\log 0.001$ .
6.
Find $\log 0.1$ , starting from $\log 10$ .
7.
Between which two whole numbers is $\log 50$ ?
1. a)2 and 3
2. b)0 and 1
3. c)5 and 6
4. d)1 and 2
8.
Estimate $\log 700$ between two whole numbers, then find it with the calculator to 3 decimal places.
9.
Use the calculator: what is $\log 250$ , rounded to 2 decimal places?
10.
A positive number $x$ has $\log x = 3$ . Find $x$ .
11.
Which value is closest to $\log 2\,000$ ?
1. a)0.301
2. b)4.301
3. c)3.301
4. d)2.301
12.
Estimate $\log 0.05$ between two whole numbers, then find it with the calculator to 3 decimal places.
13.
A positive number $x$ has $\log x = -2$ . What is $x$ ? Write it as a decimal.
14.
Write $62\,000$ in scientific notation, find the whole-number part of $\log 62\,000$ , then find $\log 62\,000$ to 3 decimal places.
15.
A whole number $N$ has $\log N \approx 5.3$ . How many digits does $N$ have?
1. a)5
2. b)53
3. c)3
4. d)6
16.
A positive number $x$ has $\log x = 2.5$ . Find $x$ , rounded to the nearest whole number.
17.
A whole number $N$ has $\log N \approx 7.48$ . How many digits does $N$ have?
18.
Use common logs to find how many times larger $100\,000$ is than $100$ .