Exponential Identities |

### Powers

**x ^{ a} x^{ b} = x^{ (a + b)}**

x^{ a} y^{ a} = (xy)^{ a}

(x^{ a})^{ b} = x^{ (ab)}

x^{ (a/b)} = b^{th} root of (x^{ a}) = ( b^{th} (x) )^{ a}

x^{ (-a)} = 1 / x^{ a}

x^{ (a – b)} = x^{ a} / x^{ b}

### Logarithms

y = log_{b}(x) if and only if x=b^{ y}

log_{b}(1) = 0

log_{b}(b) = 1

log_{b}(x*y) = log_{b}(x) + log_{b}(y)

log_{b}(x/y) = log_{b}(x) – log_{b}(y)

log_{b}(x^{ n}) = n log_{b}(x)

log_{b}(x) = log_{b}(c) * log_{c}(x) = log_{c}(x) / log_{c}(b)

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