- evaluating logarithms
- relating logarithms to exponents
- deriving laws of logarithms
- solving equations
- graphing.
| (a) |
Explain the relationship between powers, exponentials, logarithms, and radicals. |
| (b) |
Express a logarithmic expression as an exponential expression and vice versa. |
| (c) |
Determine, without technology, the exact value of a logarithm such as $log_2 8$. |
| (d) |
Explain how to estimate the value of a logarithm using benchmarks (e.g., since $log_2 8 = 3$ and $log_2 16 = 4$, $log_2 9$ is approximately equal to $3.1$ ). |
| (e) |
Derive and explain the laws of logarithms. |
| (f) |
Apply the laws of logarithms to determine equivalent expressions for given logarithmic statements. |
| (g) |
Determine, using technology, the approximate value of a logarithmic expression (e.g. $log_2 9$). |
| (h) |
Solve exponential equations in which the bases are powers of one another. |
| (i) |
Solve exponential equations in which the bases are not powers of one another. |
| (j) |
Develop, generalize, explain, and apply strategies for solving logarithmic equations and verify the solutions. |
| (k) |
Explain why a value obtained in solving a logarithmic equation may be extraneous. |
| (l) |
Solve situational questions that involve exponential growth or decay, such as loans, mortgages, and investments. |
| (m) |
Solve situational questions involving logarithmic scales, such as the Richter scale and pH scale. |
| (n) |
Analyze graphs of exponential functions of the form $y=a^x,x>0$ and report about the relationships between the value of a and the domain, range, horizontal asymptote, and intercepts. |
| (o) |
Sketch, with or without the use of technology, the graphs of exponential functions of the form $y=a^x,x>0$. |
| (p) |
Explain the role of the horizontal asymptote for exponential functions. |
| (q) |
Develop, generalize, explain, and apply strategies for sketching transformations of the graph of $y=a^x,x>0$. |
| (r) |
Analyze graphs of logarithmic functions of the form $y=log_b x,b>1$ and report about the relationships between the value of b and the domain, range, vertical asymptote, and intercepts. |
| (s) |
Sketch, with or without technology, the graphs of logarithmic functions of the form $y=log_b x,b>1$. |
| (t) |
Explain the role of the vertical asymptote for logarithm functions. |
| (u) |
Develop, generalize, explain, and apply strategies for sketching transformations of the graph of $y=log_b x,b>1$. |
| (v) |
Demonstrate graphically that $y=log_b x,b>1$ and $y=b^x,b>0$ are inverses of each other. |
