Logarithmic and Exponential Functions

An exponential function is a mathematical function of the form $$f(x) = a \times b^x$$ , where 'a' is a constant, 'b' is a positive number, and 'x' is the exponent.

A logarithm is the power to which a number must be raised to obtain another number. For example, $$\text{If } b^y = x, \text{ then } y = \text{log}_b(x)$$ .

The base of a logarithm is the number that is raised to a power. For example, in $$\text{log}_b(x)$$ , 'b' is the base.

Logarithms are the inverse operations of exponentiation. If $$b^y = x$$ , then $$y = \text{log}_b(x)$$ .

$$2^3 = 8$$ .

$$\text{log}_2(8) = 3$$ because $$2^3 = 8$$ .

It means to rewrite both sides of the equation with the same base to find the value of the variable.

The parent function of logarithmic functions is $$f(x) = \text{log}_b(x)$$ .

It reflects the graph of the logarithmic function across the x-axis.

Translating a function left means shifting it in the negative direction on the x-axis, while translating it right means shifting it in the positive direction.