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)#

1 Answer
Noah G
Nov 28, 2016

#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!

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