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

The Solve exponential equations using logarithms (base-10 and base-e) exercise is under the Algebra II Math Mission and Mathematics III 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 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.

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.