Unformatted text preview: write 129 = 2log2 (129) . We’d then have 2x = 2log2 (129) , which means our solution is x = log2 (129).
This makes sense because, after all, the deﬁnition of log2 (129) is ‘the exponent we put on 2 to get
129.’ Indeed we could have obtained this solution directly by rewriting the equation 2x = 129 in
its logarithmic form log2 (129) = x. Either way, in order to get a reasonable decimal approximation
to this number, we’d use the change of base formula, Theorem 6.7, to give us something more
calculator friendly,1 say log2 (129) = ln(129) . Another way to arrive at this answer is as follows
ln(2)
2x = 129
ln (2x ) = ln(129)
x ln(2) = ln(129)
ln(129)
x=
ln(2) Take the natural log of both sides.
Power Rule ‘Taking the natural log’ of both sides is akin to squaring both sides: since f (x) = ln(x) is a function,
as long as two quantities are equal, their natural logs are equal.2 Also note that we treat ln(2) as
any other nonzero real number and divide it through3 to isolate the variable...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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