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Indices_tut_sol1

# Indices_tut_sol1 - Indices Logarithms etc Indices...

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Indices, Logarithms, etc. Indices, Logarithms , etc. tutorial solutions 1 a) x 2x x 2x 3x 4 4 4 4 + = = b) 2x 4x 2x 4x 6x e e e e + = = c) ( 29 2 2x 2x 4x 1 e 1 2e e + = + + d) 5x 5x 4x x 4x e e e 8e 8 8 - = = 2. a) 2 2 log(abc ) loga log b logc loga log b 2logc = + + = + + b) a log loga log b logc bc = - - c) c log 3 b log 2 1 a log 2 1 c log 3 ) ab log( 2 1 c log ab log c ab log 3 3 - + = - = - = 3. a) 1 1 2 2 1 1 x 1 x 1 x exp ln exp ln 2 1 x 1 x 1 x - - - = = + + + b) ( 29 2 2ln x ln x 2 e e x = = 4. b a b log x log x log a = a) e 2 e log 3.66 1.29746 log 3.66 1.87184 log 2 0.693147 = = = b) 00311 . 1 22378 . 1 2276 . 1 4 . 3 log 293 . 0 log 293 . 0 log e e 4 . 3 - = - = = 5. ( 29 ( 29 ( 29 2 2 2log x log x 1 log(x 2) log x log x 1 log(x 2) x log log(x 2) x 1 - - = - - - = - = - - ( 29 ( 29 2 2 2 2 x x 2 x 1 x x 1 x 2 x x 3x 2 3x 2 2 x 3 = - - = - - = - + = = 6. a) 1

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Indices, Logarithms, etc. rad 180 180 1rad π = ° ° = π 3.721 180 3.721rad 213.20 × ° = = ° π b) rad 180 180 1rad π = ° ° = π ° = π ° × π = π 210 6 180 7 rad 6 7 c) rad 180 180 1rad π = ° ° = π ° = π ° × π = π 165 12 180 11 rad 12 11 7.
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Indices_tut_sol1 - Indices Logarithms etc Indices...

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