document.write( "Question 1089580: Show that logb (a) loga (b) = 1 \n" ); document.write( "

Algebra.Com's Answer #703934 by math_helper(2461) $\"\"$ $\"About$

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Say $\"+X+=+log%28a%2C%28b%29%29+\"$ \r
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\n" ); document.write( "Raise a to both sides:
\n" ); document.write( " $\"+a%5EX+=+a%5E%28log%28a%2C%28b%29%29%29+\"$
\n" ); document.write( "The right hand side is just b:
\n" ); document.write( " $\"+a%5EX+=+b+\"$
\n" ); document.write( "Now take log base b of both sides:
\n" ); document.write( " $\"+log%28b%2C%28a%5EX%29%29+=+log%28b%2C%28b%29%29+\"$
\n" ); document.write( "The left hand side is $\"+X%2Alog%28b%2C%28a%29%29+\"$ while the right hand side is 1:
\n" ); document.write( " $\"++X%2Alog%28b%2C%28a%29%29+=+1+\"$ —> $\"+log%28b%2C%28a%29%29%2AX+=+1+\"$
\n" ); document.write( "--
\n" ); document.write( "Finally, since $\"+X+=+log%28a%2C%28b%29%29+\"$ , the proof is completed by substituting for X:\r
\n" ); document.write( "\n" ); document.write( " $\"+highlight%28+log%28b%2C%28a%29%29%2Alog%28a%2C%28b%29%29+=+1%29+\"$ \n" ); document.write( "

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