How can exponential equations be solved?

Solving Exponential Equations

  1. Step 1: Express both sides in terms of the same base.
  2. Step 2: Equate the exponents.
  3. Step 3: Solve the resulting equation.
  4. Solve.
  5. Step 1: Isolate the exponential and then apply the logarithm to both sides.

What are the two methods for solving exponential equations?

How to Solve Exponential Equations

  • Equating Two Exponents with the Same Base.
  • Equating an Exponent and a Whole Number.
  • Using Logs for Terms without the Same Base.

How do you solve equations with exponential variables?

For example, to solve 2x – 5 = 8x – 3, follow these steps:

  1. Rewrite all exponential equations so that they have the same base. This step gives you 2x – 5 = (23)x – 3.
  2. Use the properties of exponents to simplify. A power to a power signifies that you multiply the exponents.
  3. Drop the base on both sides.
  4. Solve the equation.

What are exponential equations used for?

Exponential equations are indispensable in science since they can be used to determine growth rate, decay rate, time passed, or the amount of something at a given time. This module describes the history of exponential equations and shows how they are graphed.

What strategy can you use to solve an exponential equation algebraically?

In other words, when an exponential equation has the same base on each side, the exponents must be equal. This also applies when the exponents are algebraic expressions. Therefore, we can solve many exponential equations by using the rules of exponents to rewrite each side as a power with the same base.

What are the three types of exponential equations?

What Are Types of Exponential Equations?

  • The exponential equations with the same bases on both sides.
  • The exponential equations with different bases on both sides that can be made the same.
  • The exponential equations with different bases on both sides that cannot be made the same.

How do exponential functions work?

An exponential function is defined by the formula f(x) = ax, where the input variable x occurs as an exponent. The exponential curve depends on the exponential function and it depends on the value of the x. Where a>0 and a is not equal to 1. x is any real number.

What tools are used to solve exponential equations?

– Logarithms are a powerful problem-solving tool and can be used to solve exponential equations in situations when bases cannot be related. – In this method you simply use an appropriate logarithm to undo the exponent and isolate x, or you use the properties of logarithms to pull x down and solve for it.

How can exponential functions be used in solving real life problems?

Exponential functions are often used to represent real-world applications, such as bacterial growth/decay, population growth/decline, and compound interest. Suppose you are studying the effects of an antibiotic on a certain bacteria.

Why do you think it’s important to study exponential function?

Investors know the importance of an exponential function, since compound interest can be described by one. The formula A = p(1 + r)t is an exponential function in which the amount in the account (A) depends on the length of time (t) of an investment (p) deposited at a given rate (r).

How can exponential function help solve real life problems?

The best thing about exponential functions is that they are so useful in real world situations. Exponential functions are used to model populations, carbon date artifacts, help coroners determine time of death, compute investments, as well as many other applications.

What makes an equation exponential?

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable. For example, 3x = 81, 5x – 3 = 625, 62y – 7 = 121, etc are some examples of exponential equations.

How do you solve exponential equations without common bases?

In general we can solve exponential equations whose terms do not have like bases in the following way:

  1. Apply the logarithm to both sides of the equation. If one of the terms in the equation has base 10 , use the common logarithm.
  2. Use the rules of logarithms to solve for the unknown.

What makes an exponential equation?