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Precalculus

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Exponentials & Logarithms

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© The scientific sentence. 2010

Precalculus: Exponentials and logarithms



1. Recall the following properties

loga (x y ) = loga (x) + loga (y)
loga (x/y) = loga (x) - loga(y)
loga ax = x

To change the base from one to another:

loga (x) = logb (x) . loga (b)

loga (a) = 1

loga (1) = 0

loga (ax) = x

a loga(x) = x

loga (xr) = r loga (x)



2. Exercises

a) Solve for x each of the following equations:

4 e2x + 1 = 1

3 10x - 2 = 30

24 + 7 e2x + 1 = 31

e2x + 1 = - 4


b) Solve for x each of the following equations:

2 log3 (2 + 2 x) = 1

3 + 4 ln( x - 6) = 5

3 + 4 log( x + 6) = - 1

ln(x2 + ln (2 x + 2)) = 0

6 ln(x2/3) - 4 ln (x + 2) = - 2


Solutions








  
 



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