Solve equation

Question

solve (1/9)^x=-9 and (1/9)=9 for x

 

Answer 1

null set, no solutions, zero solutions, including not zero either.

(1/9)^x =-9 is impossible as a positive number such as (1/9) raised to any power is positive, there is no value of x that makes (1/9)^x = a negative number, x can be any real number, positive or negative and it doesn't make the expression negative.

take logs of both sides to get

x = log(-9) but you can't take the log of a negative number, unless you use Euler's identity.

e^ix = cosx - isinx, replace x with pi and you get

e^ipi = -1

log of both sides gives

log(-1) = ipi, an imaginary number

do the same with log(-9) and get an imaginary solution