if given log(a)=b, where no base is stated, we assume base 10, or
also, translates to/can be written equivilently as
therefore, given
where we want to find ?
assume base 10 and translate
since we cannot raise a positive number to any real power and give a negative number, ? is not a real number and therefore, there are no real solutions
if we do want to find a solution, we can use Euler's idendity
where i is the complex number i=√-1 and e is euler's number
we can try to change bases to find the value of ?
so
taking ln of both sides
using log rules
divie both side by ln(10)
in a+bi form
there are no real numbers that it evaluates to
however, it does evaluate to a complex number which is or aproximately 1.11394+1.36438i