Question

Which of the following is a solution to the equation log 6 x – log 6 (x – 1) = 1 ?

Answer 1

Is that log base 6?

Answer 2

log(sub)6 x – log(sub)6 (x – 1) = 1

Answer 3

sorry

Answer 4

\[\log_6x-\log_6(x-1)=1\]\[\log_6x/(x-1)=1\]\[\log_6x/(x-1)=\log_66\]\[x/(x-1)=6\]\[x=6(x-1)\]\[x=6x-6\]\[5x=6\]\[x=5/6\]

Answer 5

thank u

Answer 6

@ Kmousou
The LHS of the problem expression when x=5/6, as evaluated by Mathematica, is:\[-\frac{\text{Log}\left[\frac{6}{5}\right]}{\text{Log}[6]}-\frac{i \pi -\text{Log}[6]}{\text{Log}[6]}=0.898244-1.75336 I \]When evaluated at 6/5 the LHS is:\[\frac{\text{Log}\left[\frac{6}{5}\right]}{\text{Log}[6]}+\frac{\text{Log}[5]}{\text{Log}[6]}=1. \]

Answer 7

@robtobey
I don't get what you're trying to say.

Answer 8

It appears that x=6/5 is the solution, not x=5/6. Where did 6/5 come from? That is the value Mathematica comes up with when solving for x for the problem statement.

Answer 9

Solve[ Log[6, x] - Log[6, (x - 1) ] == 1, x] , x -> 6/5

Answer 10

Oh, yeah you're right, it's\[x=6/5\]