MathAdmin at 04:57, 23 October 2015

2015-10-23T04:57:03Z

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==Properties of the Logarithmic Function== In this section, we cover many properties of the logarithmic function 1. $\log_a(1) =..."$

2015-10-23T04:56:36Z

Created page with "<div class="noautonum">__TOC__</div> ==Properties of the Logarithmic Function== In this section, we cover many properties of the logarithmic function 1. <math>\log_a(1) =..."

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<div class="noautonum">__TOC__</div>
==Properties of the Logarithmic Function==

In this section, we cover many properties of the logarithmic function

1. <math>\log_a(1) = 0~ \log_a(a) = 1</math>
2. <math>a^{\log_a(M)} = M</math>
3. <math> \log_a(a^r) = r</math> (Notice this works even for a = 10)
The following properties hold for M, N, and a positive real numbers, <math> a \neq 1</math>, and r any real number
4. <math> \log_a(MN) = \log_aM + \log_aN</math>
5. <math> \log_a\left(\frac{M}{N}\right) = \log_a(M) - \log_a(N)</math>
6. <math>\log_a(M^r) = r\cdot \log_a(M)</math>
7. <math> a^r = e^{r\ln(a)}</math>
8. If <math>M = N, \text{ then }\log_a(M) = \log_a(N)</math>
9. If math>\log_a(M) = \log_a(N), \text{ then } M = N </math>

==Change of Base Formula==

The next two formulas allow us to compare logs of different bases, and are called the change of base formulas.

If <math>a, b \neq 1</math>, and M are positive real numbers, then
<math>\log_a(M) = \frac{\log_b(M)}{\log_b(N)}</math>

<math>\log_a(M) = \frac{\log(M)}{\log(a)} \text{ and } \log_a(M) = \frac{\ln(M)}{\ln(a)}</math>

[[Math_5|'''Return to Topics Page]]

@@ Line 13: / Line 13: @@
 . <math> a^r = e^{r\ln(a)}</math>
 . If <math>M = N, \text{ then }\log_a(M) = \log_a(N)</math>
-. If math>\log_a(M) = \log_a(N), \text{ then } M = N </math>
+. If <math>\log_a(M) = \log_a(N), \text{ then } M = N </math>
 ==Change of Base Formula==

Properties of Logarithms - Revision history

MathAdmin at 04:57, 23 October 2015

MathAdmin: Created page with "__TOC__ ==Properties of the Logarithmic Function== In this section, we cover many properties of the logarithmic function 1. \log_a(1) =..."

MathAdmin: Created page with "
TOC
==Properties of the Logarithmic Function== In this section, we cover many properties of the logarithmic function 1. $\log_a(1) =..."$