SOLUTION: Simplify 9log(base27)(x) - 4log(base9)(x) I didn't know how to type in a base for the logs, but i hope you can understand what I mean by (base27) I tried by having logx^9/log27

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Simplify 9log(base27)(x) - 4log(base9)(x) I didn't know how to type in a base for the logs, but i hope you can understand what I mean by (base27) I tried by having logx^9/log27      Log On


   

Question 457843: Simplify 9log(base27)(x) - 4log(base9)(x)
I didn't know how to type in a base for the logs, but i hope you can understand what I mean by (base27)
I tried by having logx^9/log27 - logx^4/logx but I didn't get anywhere...
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+9%2Alog%2827%2Cx%29+-+4%2Alog%289%2Cx%29+
(1)+9%2Alog%283%5E3%2Cx%29+-+4%2Alog%283%5E2%2Cx%29+
I'll say
+log%283%5E3%2Cx%29+=+j+
+log%283%5E2%2Cx%29+=+k+
Then
%283%5E3%29%5Ej+=+x+
+x+=+3%5E%283j%29+
and
%283%5E2%29%5Ek+=+x+
+x+=+3%5E%282k%29+
then
+3%5E%283j%29+=+3%5E%282k%29+
+3j+=+2k+
+j+=+%282%2F3%29%2Ak+
go back to (1)
(1)+9%2Alog%283%5E3%2Cx%29+-+4%2Alog%283%5E2%2Cx%29+
(1) +9%2A%282%2F3%29%2Ak+-+4k+
(1) +6k+-+4k+=+2k+
+2%2Alog%289%2Cx%29+ answer
check answer:
Let +x+=+27+
+9%2Alog%2827%2Cx%29+-+4%2Alog%289%2Cx%29+
+9%2Alog%2827%2C27%29+-+4%2Alog%289%2C27%29+
+9%2A1+-+4%2A%283%2F2%29+=+9-6+
+9+-+6+=+3+
and
+2%2Alog%289%2Cx%29+
+2%2Alog%289%2C27%29+
+2%2A%283%2F2%29+=+3+ OK