NZ Level 7 (NZC) Level 2 (NCEA)
Identify Characteristics of Logarithmic Functions
Lesson

## Exploring the log graph

The graph of the log function given by $y=\log_b\left(x\right)$y=logb(x).

When the base $b>1$b>1, the graph of the log function is a monotonically rising curve with an ever decreasing positive gradient (monotonically rising essentially means continuously rising all of the time, and an ever decreasing positive gradient means that the gradient, while never reaching zero, gradually and continuously decreases its positive steepness).

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### Outcomes

#### M7-2

Display the graphs of linear and non-linear functions and connect the structure of the functions with their graphs

#### 91257

Apply graphical methods in solving problems