# Thread: some simple logarithm questions

1. ## some simple logarithm questions

i am having some problems remebering how to do these any help would be appreciated

i) what power of 2 is equal to 37
ii) evaluate 10^2.3 and log10 0.326
iii) the power of 10 that is equal to 20
iiii) the power of 2 that is equal to 50
iiiii) log10(100)
iiiiii) log4(256)

2. Originally Posted by red55
i am having some problems remebering how to do these any help would be appreciated

i) what power of 2 is equal to 37
The log of "a" to the base "b" is the power that "b" has to be raised to
so it equals "a".

So:

b^{log_b(a)}=a

which is virtualy the definition of a logarithm.

So:

2^{log_2(37)} = 37

so here that answer is log_2(37).

Now if you want to evaluate this on a calculator we use the change of
base formula:

log_2(37) = log(37)/log(2)

where log is whatever log function you have (usually either base 10 or
natrural).

So:

log_2(37) = log(37)/log(2) ~= 3.9774.

ii) evaluate 10^2.3 and log10 0.326

These are standard operations on your calculator

iii) the power of 10 that is equal to 20
iv) the power of 2 that is equal to 50
These are both of the same form as i.

log_10(20) = log(20)/log(10)

log_2(50) = log(50)/log(2)

iiiii) log10(100)
As 10^2 = 100, no need to use a calculator here.

iiiiii) log4(256)[/quote]

4^2=16, 4^3=64, 4^4=256

RonL