Logarithms worksheet

Common log and natural ln.
First do the logs (without calculator) of integer powers of 10.
Then the logs of 1/2, 2, 20, 200, 2000. 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 lns (without calculator) of integer powers of e.
Then the others with a calculator.

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
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?

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

ln x ≈ 2.3026 log x
log x ≈ 0.4343 ln x
How are 2.3026 and 0.4343 related?

How are log 2 and log 1/2 related?
How are log 5 and log 1/5 related?
How are log e and log 1/e related?
How are ln 2 and ln 1/2 related?
How are ln 5 and ln 1/5 related?
So, in general, how are logb x and logb 1/x related?