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KEY Math 120, 123 Practice Quiz # 22 – Sections 11.5-11.6 Properties of Logarithms, Exponential and Logarithmic Equations In problems 1 and 2, use the properties of logarithms to expand the given expression. 1. log (6x2 + 12x + 6) 2. ln (e2 – 2e)3 log6 + 2log(x + 1) 3 + 3ln(e – 2) In problems 3 and 4, use the properties of logarithms to combine the given expression into a single logarithm. 3. 2 3 log( x 1) log( 2 x 2) 3 4. 3 ln( x 1) 2 ln( x 2) 4 ln( x) log( x 1) 2 / 3 2 ln ( x 1) 3 x 4 ( x 2) 2 In problems 5 and 6, use the change of base property to expand the logarithmic expressions and then evaluate the expression. 5. (log8125)(log1/58) log 125 log 8 - 3 log 8 log 15 6. log 4 36 1 log 4 6 log 36 log 4 - 2 log 1 6 log 4 In problems 7-10, solve the given equation. 7. 4 2 x 1 64 2 8. e 0.07t 3 3.08 - 36.08 9. log2(8 – 6x) = 5 -4 10. log7(x + 1) + log7(x + 2) = log76 1 11. The number of computer infected by a virus t minutes after it first appears usually increases exponentially. If the function N(t) = 100e0.077t represents the number of computers infected after t hours. a. How many computers will be infected after 2 hours? About 117 computers b. How long will it take for 80,000 computers to be infected? About 87 minutes 12. When archaeologists found the Dead Sea Scrolls, they determined that the linen wrapping had lost 22.3% of its carbon-14. How old was the linen-wrapping? 2086 years