# Exponentials and Logarithms

## Learn to Efficiently Calculate with Exponentials and Logarithms

When working with numbers, calculator users can save time by utilizing the **e** button instead of manually inputting large values.

Exponential operations have specific rules that require the bases to be identical in order to be applied.

## Understanding How Logarithms Work

Logarithms, also known as logs, are the inverse of exponential functions and are useful for solving equations with unknown exponents.

Applying Logarithms to Solve Exponentials

Logarithms can be used to find the missing exponents in exponential equations.

## Solving Exponential Equations with Examples

Example 1: Using base 5 and given an answer of 625, solve for x.

Solution: x = 4

Example 2: Given a base of 2 and an answer of 50, with an exponent of 3x + 1, find x.

Solution: x = 3

Note: When providing the solution, keep it in logarithm form when required.

## A Brief Overview of Logarithm Rules

Logarithm rules can simplify and solve complex logarithms. Similar to exponential functions, the bases must match in order to use these rules.

## Key Points to Remember when Using Exponentials and Logarithms

Exponentials and logarithms are inverse functions that use the same values to find different unknown variables. Exponentials determine the value of a constant with a given exponent, while logarithms find the exponent (power).

## Frequently Asked Questions about Exponentials and Logarithms

**Are logarithms and exponentials interchangeable?**No, they may have similarities but are used for different calculations.**What is the opposite of a logarithm?**The opposite of a logarithm is an exponential, and vice versa.**What distinguishes exponentials from logarithms?**They differ in the type of information they provide. Exponentials find the value of the base raised to a given exponent, while logarithms determine the exponent (power).**How can you convert between a logarithm and an exponential?**Since they are inverse functions, you can simply label each part of the equation and rearrange it into the other form.