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MATH 1 - 31869 Quiz X Spring 2021 Name: Date: This quiz is due by 11:59 pm Friday, May 7

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MATH 1 - 31869 Quiz X Spring 2021 Name: Date: This quiz is due by 11:59 pm Friday, May 7. Your solutions to the following problems should be complete, given in the order they are stated, and uploaded to Canvas as a single document in PDF format. √ 1. (3 points) Expand the logarithm ln(10e 5 x2 y −3 ) into a sum and difference of simpler logarithms. Use the power rule wherever possible. 2. (3 points) Condense the expression 3 log(2) − 2 log(x4 ) + π log(yz 2 ) into a single logarithm. 3. (9 points) Solve each of the following equations for x. If no solution exists or if any solutions are extraneous, state so (give exact solutions only, no decimals.) (a) 72x−1 = 343x (b) 35x−7 = e2 (c) log√2 x + log√2 (x + 3) = 4 4. (Bonus, 1 point) Simplify the expression (log2 3)(log3 4)(log4 5) · · · (log99 100) completely. x+y 1+x 5. (Bonus, 2 points) Let f (x) = log . Show that f (x) + f (y) = f . 1−x 1 + xy 1