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Units, Constants and Useful Formulas

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Logarithms and Logarithmic Equations
------------------------------------

logb(n) = e
=> be = n

Rules:

1). logb(mn) = logb(m) + logb(n)

2). logb(m/n) = logb(m) – logb(n)

3). logb(mn) = nlogb(m)

4). Change of base:  logb(x) = log(x)/log(b) or ln(x)/ln(b)

Ex 1.

27x = 92(x-7)

xlog(27) = 2(x-7)log(9)

3.3x = 4.4(x-7)

3.3x = 4.4x - 30.8

x = 30.8/1.1 = 28

or

33x = 34(x-7)

3x = 4(x - 7)

x = 28

Ex 2.

6-x = 4.8

-xln(6) = ln(4.8)

x = -ln(4.8)/ln(6) = -0.875

Ex 3.

7x = 71/5
75x = 7 => x = 2

7x = 491/5
= 72/5 => x = 0.4

32x-1 = 27
= 33
=> 2x - 1 = 3 so x = 2