Exponents, Radicals and Logarithms

Basic Algebra Review Part 1: Exponents and Logarithms (Tagalog)

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In this video
@02:30 = the correct term is commutative.

Exponents

• $(a^m)^n = a^{mn}$
• $a^m \cdot a^n = a^{m + n}$
• $\dfrac{a^m}{a^n} = a^{m - n}$
• $(ab)^m = a^m \cdot b^m$

Radicals

• $a^{1/n} = \sqrt[n]{a}$
• $a^{m/n} = \sqrt[n]{a^m}$

Logarithms

• For $y = b^x$, then $x = \log_b y$
• $\log_b x^m = m \log_b x$
• $\log_b (xy) = \log_b x + \log_b y$
• $\log_b \left( \dfrac{x}{y} \right) = \log_b x - \log_b y$
• $\log_b b = 1$
• $\log_b 1 = 0$
• $\log_e x = \ln x$
• $\log_{10} x = \log x$

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