document.write( "Question 349105: Compare equations y=log5x(the 5 is at the bottom next to the g) & y=5^x; y=log1/3x(the 1/3 is low next to the g) & y=(1/3)^x; y=log5x & y=log(1/3)x (both the 5 and 1/3 are low next to the g) \n" ); document.write( "

Algebra.Com's Answer #249580 by jsmallt9(3758) $\"\"$ $\"About$

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$\"y+=+log%285%2C+%28x%29%29\"$
\n" ); document.write( "(Note: The right side is called \"the base 5 log of x\".)
\n" ); document.write( " $\"y+=+5%5Ex\"$
\n" ); document.write( "If we rewrite the first equation in exponential form we get:
\n" ); document.write( " $\"5%5Ey+=+x\"$
\n" ); document.write( "These two equation are identical except the x's and y's have traded places. This makes the two equations inverses of each other.

\n" ); document.write( " $\"y+=+log%281%2F3%2C+%28x%29%29\"$
\n" ); document.write( " $\"y+=+%281%2F3%29%5Ex\"$
\n" ); document.write( "Again, if we rewrite the first equation in exponential form we get:
\n" ); document.write( " $\"%281%2F3%29%5Ey+=+x\"$
\n" ); document.write( "Again we have inverses.

\n" ); document.write( " $\"y+=+log%285%2C+%28x%29%29\"$
\n" ); document.write( " $\"y+=+log%281%2F3%2C+%28x%29%29\"$
\n" ); document.write( "Other than these both being logarithmic functions, there is no special relationship between these two equations. \n" ); document.write( "

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