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Last modified: January 26, 2018
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