Solving Exponential and Logarithmic Equations T

An exponential equation is an equation in which a variable appears in the exponent, typically in the form $$a^x = b$$ , where $$a$$ is a positive constant, $$x$$ is the variable, and $$b$$ is a positive number.

To convert a logarithmic equation of the form $$\text{log}_a(b) = c$$ to exponential form, rewrite it as $$a^c = b$$ .

The base of a logarithm is the number that is raised to a power to obtain a given number. In $$\text{log}_a(b)$$ , $$a$$ is the base.

The natural logarithm is the logarithm to the base $$e$$ , denoted as $$\text{ln}(x)$$ , where $$e$$ is approximately equal to 2.718.

To solve an exponential equation, isolate the exponential expression and then take the logarithm of both sides to solve for the variable.

The value of $$e^0$$ is 1, as any non-zero number raised to the power of 0 equals 1.

The inverse of an exponential function is a logarithmic function. For example, if $$y = a^x$$ , then $$x = \text{log}_a(y)$$ .

$$n = -6.326$$ .

$$a^5 = 2$$ .

$$x = 0.887$$ .