log then 2 8 6 15 3 log 2 1 log 2 4 5 log 2 1 3 log 2 4 5 log 2 4 13 5 note

Log then 2 8 6 15 3 log 2 1 log 2 4 5 log 2 1 3 log 2

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? = log ? ? then ? = ? ? + 2 = 8 ? = 6 15 3 log 2 (? − 1) + log 2 4 = 5 log 2 (? − 1) 3 + log 2 4 = 5 log 2 [4(? − 1) 3 ] = 5 note: write in exponent form log ? ? = ? then ? ? = ? 4(? − 1) 3 = 2 5 4(? − 1) 3 = 32 (? − 1) 3 = 8 ? − 1 = 2 ? = 3 19 log(2? + 1) = 1 + log(? − 2) log(2? + 1) − log(? − 2) = 1
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66 log ( 2?+1 ?−2 ) = 1 note: write in exponent form 2? + 1 ? − 2 = 10 1 2? + 1 = 10(? − 2) 2? + 1 = 10? − 20 8? = 21 ? = 21 8 26 ln(? + 1) − ln ? = 2 ln ( ? + 1 ? ) = 2 log ? ( ? + 1 ? ) = 2 ? + 1 ? = ? 2 ? + 1 = ? 2 ? ? 2 ? − ? = 1 ?(? 2 − 1) = 1 ? = 1 ? 2 − 1 28 log 2 (? + 1) + log 2 (? + 7) = 3 log 2 (? + 1)(? + 7) = 3 (? + 1)(? + 7) = 2 3 ? 2 + 8? + 7 = 8 ? 2 + 8? − 1 = 0 ? = −8 ± √8 2 − 4(1)(−1) 2(1) = −8 ± √68 2 = −8 ± 2√17 2 ? = −4 ± √ 17 29 log 1 3 (? 2 + ?) − log 1 3 (? 2 − ?) = −1
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67 log 1 3 ( ? 2 + ? ? 2 − ? ) = −1 ? 2 + ? ? 2 − ? = ( 1 3 ) −1 ? 2 + ? ? 2 − ? = 3 ? 2 + ? = 3(? 2 − ?) ? 2 + ? = 3? 2 − 3? 2? 2 − 4? = 0 2?(? − 2) = 0 ? = 0 , 2
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  • Quadratic equation, soln, L.H.S.

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