document.write( "Question 639079: find the domain of the following function in interval notation :\r
\n" ); document.write( "\n" ); document.write( "f(x)= 3√ln(x/2)
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Algebra.Com's Answer #402595 by jsmallt9(3758) $\"\"$ $\"About$

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First of all, the argument of any logarithm must be positive. So
\n" ); document.write( " $\"x%2F2+%3E+0\"$
\n" ); document.write( "which resolves to
\n" ); document.write( " $\"x+%3E+0\"$

\n" ); document.write( "Second, the radicand of a square root must not be negative. So:
\n" ); document.write( " $\"ln%28x%2F2%29+%3E=+0\"$
\n" ); document.write( "You might be able to logically dtermine from this that
\n" ); document.write( " $\"x%2F2+%3E=+1\"$
\n" ); document.write( "After all, an exponent of 0 results in 1. So any argument of 1 or greater will have an exponent greater than 0. If you can't see this then we have to solve $\"ln%28x%2F2%29+%3E=+0\"$ . We solve the inequality by rewriting it in exponential form:
\n" ); document.write( " $\"x%2F2+%3E=+e%5E0\"$
\n" ); document.write( "Since any non-zero number, including e, to the zero power is 1 this becomes:
\n" ); document.write( " $\"x%2F2+%3E=+1\"$
\n" ); document.write( "Multiplying by 2 we get:
\n" ); document.write( " $\"x+%3E=+2\"$

\n" ); document.write( "From the fact that the argument of the log had to be positive we found that
\n" ); document.write( " $\"x+%3E+0\"$
\n" ); document.write( "must be true. From the fact that radicands of square roots must bot be negative we found that
\n" ); document.write( " $\"x+%3E=+2\"$
\n" ); document.write( "must be true. Since both of these must be true, the domain must be
\n" ); document.write( " $\"x+%3E=+2\"$
\n" ); document.write( "(since any number greater than or equal to 2 must also be greater than 0). \n" ); document.write( "

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