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Published byRandell Johnston Modified over 9 years ago
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The logarithmic function log b (x) returns the number y such that b y = x. For example, log 2 (8) = 3 because 2 3 = 8. b is called the base of the logarithm.
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The natural logarithm is the logarithm with base e. e is a mathematical constant that appears in many places. It’s an irrational number, but it can be approximated as 2.72. This logarithmic function is often written ln(x). ln(x) gives you the number y such that e y = x.
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The natural logarithm has all the same useful properties as any other logarithm: ln(xy) = ln(x) + ln(y) ln(x/y) = ln(x) – ln(y) ln(x y ) = y * ln(x)
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1. What is ln(e 2 )? 2. What is ln(e)+ln(1)? 3. What is ln( )? 4. What is ln(68) – ln(25)? 5. What is ln(100)?
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1. ln(e 2 ) = 2ln(e) = 2 2. ln(1) = 0 and ln(e) = 1, so ln(e) + ln(1) = 1. 3. ln( ) = 1/2ln(e) = ½ 4. ln(68) – ln(25) = ln(68/25) = ln(2.72) ≈ 1 5. ln(100) ≈ 4.61. You’ll probably need a calculator for this one.
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