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Roots of numbers and algebraic expressions in radical form can be written in an equivalent form using rational exponents. Writing roots as exponents allows you to apply exponent rules to your work with roots.
For rational exponents:
\(a^{1/n} = a√n , a>0\)
You learned that \(a^x=b\) (exponential form) is equivalent to \(log_ab=x \space for \space a>0, \space a≠1 \space and \space b>0\)
You will be able to use your calculator to evaluate logarithms in the exam. However, you need to understand the properties of logarithms when simplifying algebraic expressions such as \(log_a^3\).
The following properties of logarithms are useful for working with logarithms but are not included in the IB formula booklet. You should memorize them or be able to derive them from the definition of a logarithm:
\(log_a1=0\)
\(log_aa=1\)
\(e^{ln (m)} = m\)
The laws of logarithms are given in the IB formula booklet and do not need to be memorized. When you use these laws it’s important to remember that they only apply to logarithms with the same base.
Exam questions involving logarithm laws will only be asked for base 10 and base e.
Logarithms can be always calculated using a calculator.
\(a^m×a^n=a^{(m+n)}\)
\(\frac{a^m}{a^n}=a^{m-n}\)
\({\left( {{a^m}} \right)^n} = {a^{m \times n}}\)
\(\left(ab\right)^m=a^mb^m\)
\({\left( {\dfrac{a}{b}} \right)^m} = \dfrac{{{a^m}}}{{{b^m}}}\)
\(a^{-m}=\frac1{a^m}\)
\(a^0=1\)
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