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

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

iv) the power of 2 that is equal to 50

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

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

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

iiiiii) log4(256)[/quote]

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

RonL