Now that I'm caught up with the current New York State Regents exams, I'm revisiting some older ones.

More Regents problems.

*Algebra 2/Trigonometry Regents, January 2013*

Part I: Each correct answer will receive 2 credits.

*26. If log 2 = a and log 3 = b, the expression log 9/20 is equivalent to
1) 2b - a + 1
2) 2b - a - 1
3) b*

^{2}- a + 10 4) 2b / (a + 1)

**Answer: 2) 2b - a - 1 **

Rewrite log 9/20 and apply the rules

= log 9 - log 20

= log 3

^{2}- log(10 * 2)

= 2 log 3 - (log 10 + log 2)

*Substitute: log 3 = b, log 10 = 1, and log 2 = a*

= 2b - (1 + a)

= 2b - 1 - a

= 2b - a - 1

*27. The expression (x + i) ^{2} - (x - i)^{2} is equivalent to
*

1) 0

2) -2

3) -2 + 4xi

4) 4xi

**Answer: 4) 4xi **

Notice that the original expression is the difference of two perfect squares and can be factored into the product of two conjugates:

(x + i)

^{2}- (x - i)

^{2}

= ((x + i) + (x - i)) ((x + i) - (x - i))

= ((2x) ((2i))

= 4xi

End of Part I.

More to come. Comments and questions welcome.

More Regents problems.

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