SOLUTION: If {{{ log ( 3,x) = M }}}, then {{{ log ( 3,1/x^2) }}} equals: A. M^2 B. 1/M^2 C. 2M D. -2M

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If {{{ log ( 3,x) = M }}}, then {{{ log ( 3,1/x^2) }}} equals: A. M^2 B. 1/M^2 C. 2M D. -2M       Log On


   

Question 945131: If +log+%28+3%2Cx%29+=+M+, then +log+%28+3%2C1%2Fx%5E2%29+ equals:
A. M^2
B. 1/M^2
C. 2M
D. -2M

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe the solution is selection D which is -2M.
here's why:
you have log3(x) = M
you also have:
log3(1/x^2) is equal to log3(1) - log3(x^2) which is equal to log3(1) - 2log3(x) which is equal to 0 - 2 * log3(x) which is equal to -2 * log3(x).
since log3(x) is given as M, the equation becomes:
log3(1/x^2) is equal to -2 * M which is equal to -2M.