Solving Exponential Equations Using Logs

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

To solve an exponential equation using logarithms, you can take the logarithm of both sides of the equation. For example, if $$a^x = b$$ , then $$x = \frac{\text{log}(b)}{\text{log}(a)}$$ .

A logarithm is the inverse operation to exponentiation, indicating the power to which a number must be raised to obtain another number. For example, $$\text{log}_a(b) = c$$ means $$a^c = b$$ .

The change of base formula states that $$\text{log}_a(b) = \frac{\text{log}_c(b)}{\text{log}_c(a)}$$ for any positive base $$c$$ .

To round a number to three decimal places, look at the fourth decimal place. If it is 5 or greater, round up the third decimal place by one. If it is less than 5, keep the third decimal place the same.

x = 3.

x = 3.

x = 1.

x = -1.42.

The natural logarithm, denoted as $$\text{ln}(x)$$ , is the logarithm to the base $$e$$ , where $$e$$ is approximately equal to 2.71828.