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section. If we start with bx logb (a) and use the Power Rule in the exponent to rewrite x logb (a) as
logb (ax ) and then apply one of the Inverse Properties in Theorem 6.3, we get
x) bx logb (a) = blogb (a = ax , 6.2 Properties of Logarithms 353 as required. To verify the logarithmic form of the property, we also use the Power Rule and an
Inverse Property. We note that
loga (x) · logb (a) = logb aloga (x) = logb (x),
and we get the result by dividing through by logb (a). Of course, the authors can’t help but point
out the inverse relationship between these two change of base formulas. To change the base of
an exponential expression, we multiply the input by the factor logb (a). To change the base of a
logarithmic expression, we divide the output by the factor logb (a). While, in the grand scheme
of things, both change of base formulas are really saying the same thing, the logarithmic form is
the one usually encountered in Algebra while the exponential form isn’t usually introduced un...
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