Question

How do you solve for x? Give any approximate result to 3 significant digits. Check your answers.

`3 log x -1 = 3 log (x-1)`

Answer 1

`x = 1.866`

Explanation:

Start by doing a little bit of algebra to isolate the logs on one side of the equation.

`3logx - 3log(x - 1) = 1`

`3(logx - log(x- 1)) = 1`

`logx - log(x - 1) = 1/3`

Use the subtraction rule of logarithms that `log_a n - log_a m = log_a (n/m)`.

`log(x/(x- 1 )) = 1/3`

`x/(x - 1) = 10^(1/3)`

`x/(x -1) = root(3)(10)`

`x = root(3)(10)(x- 1)`

`x = root(3)(10)x - root(3)(10)`

`x - root(3)(10)x = -root(3)(10)`

`x(1 - root(3)(10)) = -root(3)(10)`

`x = -root(3)(10)/(1 - root(3)(10))`

`x= 1.866`

Hopefully this helps!