Question

What are the properties of *exponents*? What are the properties of *logarithms*?

Accepted Answer

**Exponents:**       

$$a^0 = 1\;,\;a 
e 0$$     

$$x^a \cdot x^b = x^{a + b}$$   

$$x^a \div x^b = x^{a - b}$$   

$$(x^a)^b = x^{a\cdot b}$$   

$$x^{-a} = \frac{1}{x^a}$$

**Logarithms:**      

$$\log_b{1}=0$$   

$$\log_b{b}=1$$   

$$\log_b{x} + \log_b{y} = \log_b{xy}$$   

$$\log_b{x} - \log_b{y} = \log_b{\frac{x}{y}}$$   

$$\log_b{x^y} = y\log_b{x}$$   

$$\log_b{x} = \frac{\log_a{x}}{\log_a{b}}$$   

$$x^a = y$$ can be written as $$\log_x{y}=a$$, with $$y > 0$$, $$x > 0$$, and $$x 
e 1$$

Flashcard 13 - Next Generation Advanced Algebra and Functions Flashcard Set for the ACCUPLACER Test

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