How to solve for negative numbers in logarithmic equationsI am

Gregory Jones

Gregory Jones

Answered question

2022-01-20

How to solve for negative numbers in logarithmic equations
I am trying to solve the equation
zn=1.
Taking log on both sides I get nlog(z)=log(1)=0.
n=0 or z=1.
But I clearly missed out (1)even numbers which is equal to 1.
How do I solve this equation algebraically?

Answer & Explanation

Mary Herrera

Mary Herrera

Beginner2022-01-20Added 37 answers

You cant
Samantha Brown

Samantha Brown

Beginner2022-01-21Added 35 answers

Working in the reals, take the n th root of both sides.
If n is even then you'd write (zn)1n=|z|.
For example z2=1(z2)12=112|z|=1.
For odd powers, you could say, for example:
z3=1(z3)13=113z=1.
RizerMix

RizerMix

Expert2022-01-27Added 656 answers

To solve it algebraically, I'd say:
For even values of n,z=1 or z=1 are the solutions.
For odd values of n,z=1 is the answer.
And if n=0,zR would be valid as an answer.

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