SOLUTION: Solve for x: log2(log4(log5x))=-1 * the 2,4, and 5 are in the subscript therefore are the log, I am not sure if I should be converting to log ten first or how to start this prob

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve for x: log2(log4(log5x))=-1 * the 2,4, and 5 are in the subscript therefore are the log, I am not sure if I should be converting to log ten first or how to start this prob      Log On

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Question 227953: Solve for x: log2(log4(log5x))=-1
* the 2,4, and 5 are in the subscript therefore are the log, I am not sure if I should be converting to log ten first or how to start this problem.

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that log%28b%2C%28x%29%29=y can be converted to the form b%5Ey=x


log%282%2C%28log%284%2C%28log%285%2C%28x%29%29%29%29%29%29=-1 Start with the given equation.


2%5E%28-1%29=log%284%2C%28log%285%2C%28x%29%29%29%29 Use the property described above.


1%2F2=log%284%2C%28log%285%2C%28x%29%29%29%29 Rewrite 2%5E%28-1%29 as 1%2F2


log%284%2C%28log%285%2C%28x%29%29%29%29=1%2F2 Rearrange the equation.


4%5E%281%2F2%29%5E%27%27=log%285%2C%28x%29%29 Use the property described above.


sqrt%284%29=log%285%2C%28x%29%29 Convert to radical notation.


2=log%285%2C%28x%29%29 Take the square root of 4 to get 2.


log%285%2C%28x%29%29=2 Rearrange the equation.


5%5E2=x Use the property described above.


25=x Square 5 to get 25


So the answer is x=25