# Solving exponential equations

Many real world problems involve solving exponential equations. For example, to calculate how many people attended a concert or how many cars were sold on Black Friday, we need to find the solution to an equation that involves a fast-growing number. To solve these problems, you need to use both the expanded and the base form of the equation.

## Solve exponential equations

Expanded form is the usual way you might see it in an equation: To solve an exponential equation, expand both sides and then factor out a common factor. Each side will have one number multiplied by another specific number raised to a power. Then take that power and multiply it by itself (to get one number squared). That’s your answer! Base form is used for when we’re given just the base (or “base-rate”) value of something: To solve a base-rate problem, first find the base rate (number of events per unit time), then subtract that from 1. Finally, multiply the result by the event rate (also called “per unit time”).

Solving exponential equations can be a challenging task for students. However, it is important for students to understand how to solve exponential equations because they will encounter them in many different settings throughout their life. Exponential equations are used in areas such as chemistry and physics when dealing with things like growth and decay. They are also used in topics like biology and economics when discussing topics like population growth. When solving exponential equations, it is important to first determine what type of equation you are dealing with. There are three main types of exponential equations: linear, logarithmic, and power. Each of these equations has a different way of solving them, so it is important to take note of this before beginning the process. Once you have determined the type of equation you are dealing with, you can then begin by breaking down the problem into smaller pieces so that you can work on each piece individually. Once you have solved each piece of the problem individually, you can then combine all the pieces together to form a final solution for the entire problem.

Solving exponential equations can be a bit tricky. Most of the time you will need to use an inverse function to get from one number to the other. However, it is possible to solve some equations without using such techniques. Here are some examples: One way to solve an exponential equation is to use a logarithm table. For example, if you have an equation of the form y = 4x^2 + 32, then you would use the logarithm table found here. Then, you would find that log(y) = -log(4) = -2 and log(32) = 2. These values would be used in the original equation to obtain the solution: 4*y = -2*4 + 32 = -16 + 32 = 16. This value is the desired answer for y in this problem. Another way to solve an exponential equation is by using a combination of substitution and elimination. You can start by putting x into both sides of the equation and simplifying: ax + b c where a c if and only if b c/a . Then, once this is done, you can eliminate b from each side (using square roots or taking logs if necessary) to obtain a single solution that does not involve x . c if and only if , then you can substitute for y in both sides, thus eliminating x

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