SOLUTION: solve the logarithmic equation as shown: log9 (x-6) - log9 x=1 I got the answer to be -4/7

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve the logarithmic equation as shown: log9 (x-6) - log9 x=1 I got the answer to be -4/7      Log On


   



Question 1082338: solve the logarithmic equation as shown:
log9 (x-6) - log9 x=1
I got the answer to be -4/7

Found 3 solutions by josgarithmetic, MathLover1, MathTherapy:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
9%5E1=%28x-6%29%2Fx---------... do you see how?

x-6=9x
.
.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%289%2C+%28x-6%29%29-log%289%2C+x%29=1+

log%289%2C+%28x-6%29%2Fx%29=1+....convert in base 10

log%28%28x-6%29%2Fx%29%2Flog%289%29=1+

log%28%28x-6%29%2Fx%29=log%289%29+.......if log same, than we have

%28x-6%29%2Fx=9+

x-6=9x+

-6=9x-x+

-6=8x+

x=-6%2F8+

x=-3%2F4+





Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!

solve the logarithmic equation as shown:
log9 (x-6) - log9 x=1
I got the answer to be -4/7
That's incorrect!
log+%289%2C+%28x+-+6%29%29+-+log+%289%2C+%28x%29%29+=+1
log+%289%2C+%28x+-+6%29%2Fx%29+=+1 ------ Applying log+%28a%2C+%28b%29%29+-+log+%28a%2C+%28c%29%29+=+log+%28a%2C+%28b%2Fc%29%29
%28x+-+6%29%2Fx+=+9%5E1 ------ Expressing in EXPONENTIAL form
9x = x - 6 ------ Cross-multiplying
9x - x = - 6
8x = - 6
highlight_green%28matrix%281%2C5%2C+x%2C+%22=%22%2C+-+6%2F8%2C+or%2C+-+3%2F4%29%29
That's how easy this is!!