## Friday, October 01, 2021

### Algebra 2 Problems of the Day (Algebra 2/Trigonometry Regents, January 2013)

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

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) b2 - a + 10
4) 2b / (a + 1)

Answer: 2) 2b - a - 1

Rewrite log 9/20 and apply the rules

log 9/20
= log 9 - log 20
= log 32 - 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

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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