Solving Exponential equations without log

• An exponential equation involves an unknown variable in the exponent. In this lesson, we will focus on the exponential equations that do not require the use of logarithm. In algebra, this topic is also known as solving exponential equations with the same base. Why? The reason is that we can solve the equation by forcing both sides of the exponential equation to have the same or equal base.

Key Steps in Solving Exponential Equations without Logarithms

Make the base on both sides of the equation the SAME

Basic Properties of Exponents

1) Zero Property

2) Negative Exponent Property

3) Product Rule

4) Quotient Rule

5) Power to a Power Rule

REAL WORLD APPLICATION

Logarithms put numbers on a human-friendly scale.

Large numbers break our brains. Millions and trillions are "really big" even though a million seconds is 12 days and a trillion seconds is 30,000 years. It's the difference between an American vacation year and the entirety of human civilization.

The trick to overcoming "huge number blindness" is to write numbers in terms of "inputs" (i.e. their power base 10). This smaller scale (0 to 100) is much easier to grasp:

SAT PROBLEM