How do you solve 12(14x)=18?

1 Answer
Jul 31, 2016

x=12+(2k+1)πiln(4) for any integer k

Explanation:

Divide both sides by 12 to get:

14x=1812=32

Add 4x32 to both sides to get:

12=4x

For any Real value of x, 4x>0, so it cannot equal 12.

If we had wanted 4x=12 then we could have found:

21=12=4x=(22)x=22x

and hence solution x=12.

We can make this into a set of Complex solutions for our original problem by adding an odd multiple of πiln(4)

Let x=12+(2k+1)πiln(4) for any integer k

Then:

4x=412+(2k+1)πiln(4)

=4124(2k+1)πiln(4)

=12(eln(4))(2k+1)πiln(4)

=12eln(4)(2k+1)πiln(4)

=12e(2k+1)πi

=12(eπi)2k+1

=12(1)2k+1

=12