Logarithms worksheet

Common log and natural ln.
First do the logs (without calculator) of integer powers of 10.
Then the lns (without calculator) of integer powers of e. And ln e^e
Then with calculator the logs of 1/2, 2, 20, 200, 2000. Notice the pattern!
Without calculator, what is log 20,000:_____
Then the logs of the "fives" : 1/5, 5, now continue without calculator: 50, 500, 5000.
Then the remainder with a calculator.

Note that x increases going down the table.

x	log x	ln x
.01
.1
1/e²=e^-2 ≈
.2 =1/5
1/e=e^-1 ≈
.5 =1/2
1
2
e ≈
5
e² ≈
10
e^e ≈
20
e³ ≈
50
e⁴ ≈
100
e⁵ ≈
200
500
1000
2000
5000
10000

e < 10 so for x>1 is ln x less than log x?

How are log 2 and log 1/2 related?
How are log 5 and log 1/5 related?
How are log 10 and log 1/10 related?
How are log 100 and log 1/100 related?
How are ln 2 and ln 1/2 related?
How are ln 5 and ln 1/5 related?
So, in general, how are log_b x and log_b 1/x related?

Look at log e. Now do: 1 / log e =
Look at ln 10. Now do: 1 / ln 10 =
How are log e and ln 10 related?
How are 2.3026 and 0.4343 related?
ln x = log x / log e = log x · 1/log e ≈ 2.3026 log x
log x = ln x / ln 10 = ln x · 1/ln 10 ≈ 0.4343 ln x

For every pair of log x and ln x what are the ratios:
ln x / log x =
log x / ln x =