Solve exponential equations using logarithms (base-10 and base-e)

The  exercise is under the Algebra II Math Mission. This exercise practices solving exponential equations that have 10 or e at the base of the exponential term.

Types of Problems
There is one type of problems in this exercise:


 * 1) Solve the equation for ___. Express the solution as a logarithm in base-10, then approximate the value of w. Round the answer to the nearest thousandth.: This problem presents an exponential expression. The student is asked to express it as a logarithm in base-10, then approximate the value of the variable .Solve exponential equations using logarithms (base-10 and base-e).PNG

Strategies

 * 1) To solve an exponential equation, students must first isolate the exponential part.
 * 2) Then, they can solve for the exponent by converting the equation to logarithmic form using the following equivalence: $$b^t=a \text{ if and only if } \text{log}_{b}a=t$$

Real-life Applications

 * 1) Exponents are used in Computer Game Physics, pH and Richter Measuring Scales, Science, Engineering, Economics, Accounting, Finance, and many other disciplines.
 * 2) Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas.
 * 3) Exponential Decay is associated with Light, Sound, Sporting Fixtures, Dangerous Chemicals, and Radioactive Waste.
 * 4) People who use Exponents are Economists, Bankers, Financial Advisors, Insurance Risk Assessors, Biologists, Engineers, Computer Programmers, Chemists, Physicists, Geographers, Sound Engineers, Statisticians, Mathematicians, Geologists and many other professions.