In other words, the log rule will let us move the variable back down onto the ground, where we can get our hands on it. Content Continues Below. In this particular instance, since the base is 10 and since base- 10 logs can be done on the calculator, I will use the common log instead of the natural log to solve this particular equation:. When I take the log of both sides of an equation, I can use any log I like base- 10 log, base- 2 log, natural log, etcbut some are sometimes more useful than others. This is not generally required, but is often more useful than other options. One property of exponential equations that is initially confusing to some students is determining how many solutions an equation will have. In order to better understand the division of exponents, consider the following example, which is solved in two ways to provide a more thorough understanding of how to divide exponents.

In this section we will look at solving exponential equations and we will look at solving logarithm equations in the next section.

Video: Exponential equation algebraically Solving Exponential Equations

There are two. SOLVING EXPONENTIAL EQUATIONS. To solve an exponential equation, take the log of both sides, and solve for the variable.

Example 1: Solve for x in the. Solve exponential equations using exponent properties. Google Classroom Facebook Twitter. Email. You might need: Calculator.

I will use the natural log in this case:. In order to better understand the division of exponents, consider the following example, which is solved in two ways to provide a more thorough understanding of how to divide exponents. In order to better understand how these formulas could be used to multiply exponents, consider the following example:.

Rewrite both sides to have the same base since both sides are multiples of 8.

## Solve exponential equations using exponent properties (advanced) (practice) Khan Academy

While there is no formula for solving an exponential equation, the following examples provide some insight into common techniques used in finding the unknown value in an exponential equation. Since the powers must be the same, then we can set the two powers equal to each other, and solve the resulting equation. Share This Page.

### Solve exponential equations using exponent properties (practice) Khan Academy

Demonstrates how to solve exponential equations by using logarithms. Explains how to recognize when logarithms are necessary. Provides worked examples.

When asked to solve an exponential equation such as 2 look at the base of the exponential equation and determine if the each side of the problem can be.

In solving these more-complicated equations, you will have to use logarithms.

## Exponential Equations GMAT Math Study Guide

There are many laws of exponents that should be memorized and practiced in order to be thoroughly understood. Most exponential equations do not solve neatly; there will be no way to convert the bases to being the same, such as the conversion of 4 and 8 into powers of 2. The power on the left-hand side of the original equation would simplify as:.

Video: Exponential equation algebraically How do you solve an exponential equation with e as the base

The process would have been exactly the same, and the eventual answer would have been equivalent. First, we'd need to apply the change-of-base formula to convert the expression into something in a base that our calculators can understand; namely, the natural log or the common log.

Web Design by. So the answer here is: no solution. By taking the log of an exponential, we can then move the variable being in the exponent that's now inside a log out in front, as a multiplier on the log.

The right-hand side is easy:. Either way, I get the same answer, but taking natural log in the first place was simpler and shorter.

Then my confirmed solution is:. Terms of Use Privacy Contact.

Before I can start looking at the exponential, I first have to get rid of the 3so I'll divide that off to get:. This solution demonstrates the logical basis for how this entire class of equation is solved: If the bases are the same, then the powers must also be equal; this is the only way for the two sides of the equation to be equal to each other.

One of the more commonly tested properties of exponents and exponential equations is that an even exponent hides the sign of its roots.

For a more detailed explanation of this technique, please visit the factoring study guide and the quadratic equations study guide. A number can never go from positive to negative by taking powers; I can never turn a positive two into a negative anythingfour or otherwise, by multiplying two by itself, regardless of the number of times I do the multiplication.

Note: You could also solve the above by using exponent rules to break apart the power on the 2 :.