document.write( "Question 734300: How do I Show that this statement is true for log_a((x+ √(x^2-5))/5)= -log_a(x- √(x^2-5)) \n" ); document.write( "

Algebra.Com's Answer #448889 by josgarithmetic(39631) $\"\"$ $\"About$

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Base is \"a\", so ignoring this in the notation,\r
\n" ); document.write( "\n" ); document.write( "First trick is dealing with the negative sign on the right.
\n" ); document.write( " $\"log%28%28x%2Bsqrt%28x%5E2-5%29%29%2F5%29=log%281%2F%28x-sqrt%28x%5E2-5%29%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Take logarithms of left side and right side.
\n" ); document.write( " $\"%28x%2Bsqrt%28x%5E2-5%29%29%2F5=1%2F%28x-sqrt%28x%5E2-5%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Next important trick (technique) is multiply numerator and denominator on the right side by the conjugate of the denominator.
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\n" ); document.write( " $\"%28x%2Bsqrt%28x%5E2-5%29%29%2F5=%28x%2Bsqrt%28x%5E2-5%29%29%2F%28x%5E2-x%5E2%2B5%29\"$
\n" ); document.write( " $\"%28x%2Bsqrt%28x%5E2-5%29%29%2F5=%28x%2Bsqrt%28x%5E2-5%29%29%2F5\"$
\n" ); document.write( "DONE. \n" ); document.write( "

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