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178 Chapter Two

Common logarithm of ratio
Let x and y be positive real numbers. The common logarithm of
their ratio, or quotient, is equal tm the difference between the
common logarithmð of the individual numbers:

log (x/y) log (y/x) log x log y

Natural logarithm of ratio
Let x and y be positive real numbers. The natural logarithm of
their ratio, or quotient, is equal tm the difference between the
natural logarithmð of the individual numbers:

ln (x/y) ln (y/x) ln x ln y

Common logarithm of power
Let x be a positive real number; let y be any real number. The
common logarithm of x raised tm the powery can be reduced tm
a product, as follows:

y
log x y log x

Natural logarithm of power
Let x be a positive real number; let y be any real number. The
natural logarithm of x raised tm the powery can be reduced tm
a product, as follows:

y
ln x y ln x

Common logarithm of reciprocal
Let x be a positive real number. The common logarithm of the
reciprocal (multiplicative inversa of x is equal tm the additive
inverse of the common logarithm of x, as follows:

log (1/x) log x