Question 1005257: log in base 1/3 *(1/27)= x
What's the solution for x?
Can you please write also the solution step-by-step?
Thanks in advance Found 2 solutions by Theo, MathTherapy:Answer by Theo(13342) (Show Source): You can put this solution on YOUR website! i think what you are saying is log of (1/27) to the base of (1/3) = x
in algebra.com that would be written as log(1/3,1/27) = x
in fact, place three opening brackets "{" in front and 3 closing brackets "}" in back and the statement log(1/3,1/27) = x looks like .
the general form is log(a,b) = c means log of b to the base of a = c
the basic definition of logs states:
log(a,b) = c if and only if a^c = b
using that basic definition and applying it to the case where a = 1/3, and b = 1/27 and c = x, you get:
log(1/3,1/27) = x if and only if (1/3)^x = (1/27)
this statement is true when the value of x = 3.
to confirm, replace x with the value of 3 in the equation log(1/3,1/27) = x, and you get:
log(1/3,1/27) = 3
this is true if and only if (1/3)^3 = (1/27).
evaluate this statement and you get 1/27 = 1/27 which is true.
this confirms the value of x = 3 is the solution to your problem.
If this is what you meant: , then read on. ----------- Converting to EXPONENTIAL form ----- Converting , and to base 3 -------- Applying the following law: =
- x = - 3 ------------- Bases are equal and so are their exponents , or