SOLUTION: Write the equation 125^4/3=625 in logarithmic form. (A) log [625]125=3/4 (B) 2log[4]625=125 (C) log[4/3]625 =125 (D) log [125]625=4/3 Thank you!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Write the equation 125^4/3=625 in logarithmic form. (A) log [625]125=3/4 (B) 2log[4]625=125 (C) log[4/3]625 =125 (D) log [125]625=4/3 Thank you!      Log On


   

Question 31890: Write the equation 125^4/3=625 in logarithmic form.
(A) log [625]125=3/4
(B) 2log[4]625=125
(C) log[4/3]625 =125
(D) log [125]625=4/3
Thank you!
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
+125%5E%284%2F3%29+=+625++.

Lets take logs to base125 --> written as log_125

+log_125%28125%5E%284%2F3%29%29+=+log_125%28625%29++
+%284%2F3%29log_125%28125%29+=+log_125%28625%29++

now log to base 125 of 125 is 1 --> log_125(125) = 1 since log_a(a) is always 1, irrespective of the value of a.

+%284%2F3%29+=+log_125%28625%29++ --> this is an answer.
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How about taking logs to base 625?

+log_625%28125%5E%284%2F3%29%29+=+log_625%28625%29++
+%284%2F3%29log_625%28125%29+=+1++
+log_625%28125%29+=+%283%2F4%29++ --> this is an answer too.

So either A or D is correct.

jon.