$$\log_n(y) = \log_n(a) + x \log_n(b)$$\n$$y = (\log_n b)x + \log_n(a)$$

$$y = mx + b$$

$$m = \frac{\log(y_2) - \log(y_1)}{x_2 - x_1}$$

$$a = n^b$$, where n is the base of the logarithm.

$$y = 10^{mx+b}$$ (if base 10 logarithm)

$$y = ae^{kt}$$, where a is the initial value, k is the growth rate, and t is time.

$$y = ae^{-kt}$$, where a is the initial value, k is the decay rate, and t is time.

The slope and y-intercept of the linearized equation can be used to determine the parameters of the original exponential equation.

$$\log(ab) = \log(a) + \log(b)$$

$$\log(a^x) = x\log(a)$$

Indicates an exponential relationship between the x and y variables.

A faster rate of exponential growth or decay.

Indicates that the y-value is constant (no growth or decay).

Find the y-intercept of the linearized data and calculate its antilog.

Exponential growth.

Exponential decay.

Different bases will change the scale of the y-axis, affecting the slope's numerical value but not the overall trend.

The relationship is not purely exponential; it may be polynomial, logarithmic, or a combination of functions.

Compare the slopes of the lines representing each dataset. The steeper the slope, the faster the growth rate.

The data may have some error or noise, or the relationship may not be perfectly exponential.

A graph with one logarithmic axis and one linear axis.

The y-axis represents the logarithm of the data values.

Exponential data.

To visualize data with a wide range of values and identify exponential trends.

Transforming exponential data into a linear form by taking the logarithm of the dependent variable.

The rate of growth or decay of the exponential function.

The logarithm of the initial value of the exponential function.

A linear scale has equal intervals, while a logarithmic scale compresses larger values.

Base 10 or base e (natural logarithm).

The x-axis is always on a linear scale.