SOLUTION: (log4(log4^x))=-4

Question 238662: (log4(log4^x))=-4
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

Solving equations of the form
log(some-expression-with-a-variable) = another-expression
is usually done by rewriting the equaiton in exponential form. To rewrite logarithmic equations in logarithmic form we need to remember that is equivalent to

Since your equation has a logarithm within a logarithm, we will have to do this twice. Rewriting the outer logarithm in exponential form we get:

Since and , the right side simplifies to:

Now we will rewrite the remaining logarithm in exponential form:

This may be an acceptable form for the answer. But it can be simplified a little. First we can "reduce" the exponent using a bit of cleverness and a good understanding of fractional exponents:
Factor the exponent:

Use the property to rewrite the abvoe as a power of a power:

Since and , we can replace with 2. (This is why we factored 1/2 out of the exponent.)

This is a simplified form of the answer. With a fractional exponent, we could write this in radical form:

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