SOLUTION: 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

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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) About Me  (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 log%281%2F3%2C1%2F27%29+=+x.

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.








Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

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
If this is what you meant: log+%281%2F3%2C+%281%2F27%29%29+=+x, then read on.
%281%2F3%29%5Ex+=+1%2F27 ----------- Converting to EXPONENTIAL form
%283%5E-1%29%5Ex+=+3%5E-+3----- Converting 1%2F3, and 1%2F27 to base 3
3%5E%28-+x%29+=+3%5E+-+3 -------- Applying the following law: %28a%5Eb%29%5Ec = a%5E%28bc%29
- x = - 3 ------------- Bases are equal and so are their exponents
x+=+%28-+3%29%2F%28-+1%29, or highlight_green%28x+=+3%29