Key Concepts
- A percent is the ration of a number and 100.
- To find a percent of a whole, write the percent as a decimal by moving the decimal two places to the left, then multiply the percent by the whole amount.
- By the addition property of equality, the same amount can be added or subtracted to both sides of an equation without changing the value of the equation.
- By the multiplication property of equality, the same amount can be multiplied or divided to both sides of an equation without changing the value of the equation.
- Solving Multi-step Equations
1. (Optional) Multiply to clear any fractions or decimals.
2. Simplify each side by clearing parentheses and combining like terms.
3. Add or subtract to isolate the variable term—you may have to move a term with the variable.
4. Multiply or divide to isolate the variable.
5. Check the solution. - When solving equations in which the variable is contained in an exponent, first isolate the exponent term, then take the logarithm on both sides. Apply the power rule of logarithms, then the multiplication property of equality to isolate the variable.
Key Expressions, Equations, and Inequalities
- [latex]a(b+c)=ab+ac[/latex]
- [latex]\log\left(M^{n}\right)=n\log M[/latex]
- [latex]\dfrac{\log M}{\log N} = \dfrac{\ln M}{\ln N} [/latex]
Glossary
- logarithm
- a number [latex]\log_{b}M[/latex]
- common logarithm
- a logarithm with base [latex]b=10[/latex], [latex]\log M[/latex]
- natural logarithm
- a logarithm with base [latex]b=e[/latex], [latex]\ln M[/latex]
