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Examples on Log rules:
Example: Calculate (1/3)log10 2.
Solution: logb n√A = logb A1/n = (1/n)logb A
(1/3)log10 2
= log10 3√2
= log10 1.259
= 0.1003
Example: Calculate log10 1.
Solution:
Rule 6. logb 1 = 0
log10 1 = 0
Example: Calculate -log10 2.
Rule 7: logb (1/A) = -logbA
-log10 2
= log10 (1/2)
= -log10 0.5
= -0.3010
∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
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-1+5-100=?
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