Unformatted text preview: og(x)
y=
1 − log(x)
log(y )
x=
Interchange x and y .
1 − log(y )
x (1 − log(y )) = log(y )
x − x log(y ) = log(y )
x = x log(y ) + log(y )
x = (x + 1) log(y )
x
= log(y )
x+1
x
y = 10 x+1
Rewrite as an exponential equation.
3 Refer to page 158 for a discussion of what this means. 374 Exponential and Logarithmic Functions
x We have f −1 (x) = 10 x+1 . Graphing f and f −1 on the same viewing window yields y = f (x) = x
log(x)
and y = g (x) = 10 x+1
1 − log(x) 6.4 Logarithmic Equations and Inequalities 6.4.1 375 Exercises 1. Solve the following equations analytically.
x
= 150
10−12
(j) log3 (x) = log 1 (x) + 8 (a) log 1 x = −3 (i) 10 log 2 (b) ln(x2 ) = (ln(x))2 3 (c) log3 (x − 4) + log3 (x + 4) = 2
(d) log5 (2x + 1) + log5 (x + 2) = 1
(e) log2 (x3 ) = log2 (x)
(f) log169 (3x + 7) − log169 (5x − 9) =
x
(g) log
= 4.7
10−3
(h) − log(x) = 5.4 1
2 1
3x − 2
=
(k) log125
2x + 3
3
(l) ln(x + 1) − ln(x) = 3
(m) ln(ln(x)) = 3
(n) 2 log7 (x) = log7 (2) + log7 (x + 12)
(o)...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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