log (base a) of 2 = .6055
log (base a) of 3 = .9597
log (base a) of 10 = 2.0115
i need to find the value of log (base a) of 7. the problem is that i can't seem to find any combination of 2, 3 and, 10 multiplied/divided together that would make 7.
log (base a) of 2 = .6055
log (base a) of 3 = .9597
log (base a) of 10 = 2.0115
i need to find the value of log (base a) of 7. the problem is that i can't seem to find any combination of 2, 3 and, 10 multiplied/divided together that would make 7.
see this, Dunham, William - Euler - The Master of Us All - (1999), page 17. It may help
7 is prime not a factor of 2, 3 and 10.
That is why you can not use the properties of LOGARITHM to obtain a pattern for base b.
But it is still solvable, Euler's Formula, log (base b) of 2 = (ln 2)/(ln b)
1. log(base a) 2 = 0.6055
a^(0.6055) = 2
a = 2^(1/0.6055) = 3.1416 = pi
2. log (base a) of 3 = .9597
a = 3^(1/0.9597) = 3.1416
Thus, N = log (base a) 7 = log (base pi) 7 = log 7/log pi = log 7/ log 3.1416 = 1.69988 = 1.7