Page 128 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, College Preparation
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
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Sample problem: Why is it possible to determine log10(100) but not log10(0) or log10(–100)? Explain your reasoning.
2.4 determine, with technology, the approximate logarithm of a number to any base, including base 10 [e.g., by recognizing that log10(0.372) can be determined using the LOG key on
a calculator; by reasoning that log329 is between 3 and 4 and using systematic trial to determine that log329 is approximately 3.07]
2.5 make connections between related logarithmic and exponential equations (e.g., log5125 = 3 can also be expressed as 53 = 125), and solve simple exponential equations by rewriting them in logarithmic form (e.g., solving 3x = 10 by rewriting the equation as log3 10 = x)
2.6 pose problems based on real-world applica- tions that can be modelled with given expo- nential equations, and solve these and other such problems algebraically by rewriting them in logarithmic form
Sample problem: When a potato whose tem- perature is 20°C is placed in an oven main- tained at 200°C, the relationship between the core temperature of the potato T, in degrees Celsius, and the cooking time t, in minutes, is modelled by the equation 200 – T = 180(0.96)t . Use logarithms to determine the time when the potato’s core temperature reaches 160°C.