Question

express the given logarithm in terms of common logarithms. then approximate its value to four decimal places.
log2 3.2 ?

Answer 1

@bmorse

Answer 2

@jdoe0001

Answer 3

Can you think of a number which is a power of 2 which when divided by a power of 10 will give you 3.2?

Answer 4

You can write the log of a quotient as the difference of the log of the numerator and the log of the denominator:

\[\log{\frac{a}{b}} = \log a-\log b\]

Answer 5

And you can change bases of logs with the change of base property:
\[\log_b x = \frac{\log_a x}{\log_a b}\]

Answer 6

so what numbers go where @whpalmer4

Answer 7

well, first, did you think of those numbers I requested?

Answer 8

Powers of 2:

2 4 8 16 32 64 128 256 etc.

Powers of 10:
10 100 1000 etc.

Anything jumping out at you?

Answer 9

no?? @whpalmer4

Answer 10

Find a number on the first list (powers of 2) which can be divided by a number on the second list (powers of 10) and yield the result 3.2.

Answer 11

The goal here is to find numbers which have "easy" logs to compute in either base 2 or base 10.

Answer 12

I think you'll take the log2/log3.2 =0.59592202035

Answer 13

I mean log3.2/log2, i think you switch them.

Answer 14

I get 1.67807190511 or 1.6781

Answer 15

\[log_2 3.2 = \log_2 \frac{32}{10} = \log_2 32 - \log_2 10 = \log_2 32 - \frac{\log_{10}10}{\log_{10}2} = 5 - \frac{1}{0.30103} =\]

Answer 16

\[\log_2 32 = 5\]because \[2^5=32\]\[\log_{10} 10 = 1\] because\[10^1=10\]
\[\log_{10}2 \approx 0.30103\]I just happen to know that, like I know the natural and common logs of 2,3,5,7, which allows me to find the logs of many other numbers by doing simple arithmetic. For example, \(\log_{10} 8 = 3*\log_{10}2\approx 0.90309\) because \(8=2^3\)

Answer 17

and \[\log a^b = b\,\log a\]

Answer 18

http://campuses.fortbendisd.com/campuses/documents/Teacher/2009/teacher_20090408_1245.pdf

Look at #9 and #10, answers are at the bottom.