Solving & Graphing Exponential Equations

An exponential equation is an equation in which a variable appears in the exponent. For example, $$2^x = 8$$ .

The general form of an exponential function is $$y = ab^x$$ , where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

An asymptote is a line that a graph approaches but never touches. For exponential functions, the horizontal asymptote is often the line $$y = 0$$ .

To solve an exponential equation with the same base, set the exponents equal to each other. For example, if $$2^x = 2^5$$ , then $$x = 5$$ .

The base of the exponential function $$y = 2^x$$ is 2.

To rewrite a number as a power of another number, express it in terms of the base. For example, $$8 = 2^3$$ .

The solution is $$x = -\frac{4}{5}$$ .

The y-intercept is the point where the graph crosses the y-axis, which occurs at $$(0, a)$$ in the function $$y = ab^x$$ .

A negative exponent indicates a reciprocal. For example, $$b^{-n} = \frac{1}{b^n}$$ .

The horizontal asymptote is $$y = 2$$ .