# Exponential Problem Solving

It's an equation that has exponents that are $$\red$$.

$$\red 4^3 = \red 2^x$$ $$\red 9^x = \red$$ $$\left( \red \right)^ = \red 4^3$$ $$\red 4^ 1 = \red$$ In each of these equations, the base is different.

These types of equations are used in everyday life in the fields of Banking, Science, and Engineering, and Geology, as well as more fields.

We learned about the properties of exponents here in the Exponents and Radicals in Algebra Section, and did some solving with exponents here.

Check out these kinds of exponential functions in this tutorial!

If something decreases in value at a constant rate, you may have exponential decay on your hands.

Exponential functions often involve the rate of increase or decrease of something.

When it's a rate of increase, you have an exponential growth function!

Remember that exponential functions are named that because of the “$$x$$” in their exponents! “$$b$$” is called the base of the exponential function, since it’s the number that is multiplied by itself “$$x$$” times (and it’s not an exponential function when $$b=1$$).

$$b$$ is also called the “growth” or “decay” factor.

## Comments Exponential Problem Solving

• ###### Examples of Solving Logarithmic Equations
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Rewrite the problem in exponential form by moving the base of the logarithm to the other side. Simplify the problem by distributing and squaring the 6. Solve the problem by subtracting 36 from each side to ge t it equal to zero, and then factoring or using the quadratic formula to find the values of x.…

• ###### Working with Exponents and Logarithms - Math Is Fun
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Working with Exponents and Logarithms. Always try to use Natural Logarithms and the Natural Exponential Function whenever possible. Solve 2 log 8 x = log 8 16.…

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Chapter 6 Exponential Functions and Sequences Mathematical Practices Problem-Solving Strategies Mathematically profi cient students look closely to fi nd a pattern. Monitoring Progress 1. A rabbit population over 8 consecutive years is given by 50, 80, 128, 205, 328, 524, 839, 1342. Find the population in the tenth year. 2.…

• ###### Exponential and Logarithmic Equations College Algebra
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Do all exponential equations have a solution? If not, how can we tell if there is a solution during the problem-solving process? No. Recall that the range of an exponential function is always positive. While solving the equation we may obtain an expression that is undefined.…

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Step 6 Finish solving the problem by isolating the variable. Steps for Solving Exponential Equations with the Same Base Step 1 Determine if the numbers can be writ ten using the same base. If so, go to Step 2. If not, stop and use Steps for Solving an Exponential Equation with Different Bases.…

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Solving Exponential Equations. Solving for Time and Rates. More Ways to Use This Stuff. Tricks to Help with Solving Log Equations. Solving Log Equations. Exercises…

• ###### Solving Exponential and Logarithmic Equations
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Solve exponential equations. Solve logarithmic equations. Solve exponential and logarithmic inequalities. Solving Exponential Equations Exponential equations are equations in which variable expressions occur as exponents. The result below is useful for solving certain exponential equations. The preceding property is useful for solving an.…

• ###### Exp & Log Problem Solving - PreCalculus
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Fpc_unit_7.3_ecorrective_exp_and_log_problem_solving.pdf File Size 2570 kb File Type pdf…

• ###### Solving Exponential Equations - Cool Math
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Solving Exponential Equations. We HAVE to solve for Mr. t. I pity the fool who can't solve Mr. t! Pity the fool! Sorry for the lame A-Team joke.…

• ###### Quiz & Worksheet - Solving Exponential Equations
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Problem solving - use acquired knowledge to solve an exponential equation practice problem about saving to buy a car using interest from money in the bank Additional Learning…