SOLUTION: For what values(s) of x does {{{log(2,(log(3,(log(4,(x)))^"")))}}}{{{""=""}}}{{{0}}}?

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Question 1043592: For what values(s) of x does log%282%2C%28log%283%2C%28log%284%2C%28x%29%29%29%5E%22%22%29%29%29%22%22=%22%220?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C%28log%283%2C%28log%284%2C%28x%29%29%29%5E%22%22%29%29%29%22%22=%22%220

We use the definition of logs, which is the rule for changing
logarithmic equations to or from exponential equations:

Definition of logs:  If log%28B%2C%28A%29+%29%22%22=%22%22C, then A%22%22=%22%22B%5EC


log%282%2C%28log%283%2C%28log%284%2C%28x%29%29%29%5E%22%22%29%29%29%22%22=%22%220

Using the definition of logs:

log%283%2C%28log%284%2C%28x%29%29%29%29%22%22=%22%222%5E0

log%283%2C%28log%284%2C%28x%29%29%29%29%22%22=%22%221

Using the definition of logs again:

log%284%2C%28x%29%29%22%22=%22%223%5E1

log%284%2C%28x%29%29%22%22=%22%223
Using the definition of logs once more:

x%22%22=%22%224%5E3

x%22%22=%22%2264

Edwin