Solving Natural Logarithms | MathHelp.com - By MathHelp.com
| 00:0-1 | in this example were asked to solve each of the | |
| 00:02 | following equations for X and leave our answers in terms | |
| 00:07 | of E . To solve for X . In the | |
| 00:10 | first equation L N x equals three . We simply | |
| 00:15 | switch the equation from log arrhythmic to exponential form . | |
| 00:21 | Remember that ? L . N . X means the | |
| 00:24 | natural log of X . And a natural log has | |
| 00:28 | a base of E . So to convert the given | |
| 00:32 | equation to exponential form , remember that the base of | |
| 00:37 | the log represents the base of the power , The | |
| 00:40 | right side of the equation represents the exponents and the | |
| 00:45 | number inside the log represents the result . So we | |
| 00:49 | have E . To the 3rd equals x . And | |
| 00:54 | we've solved for X notice that our answer E cubed | |
| 01:00 | is written in terms of E , which is what | |
| 01:03 | the problem asks us to do . Now let's take | |
| 01:07 | a look at the second equation . Ln x squared | |
| 01:12 | equals eight . Again we saw for X by switching | |
| 01:17 | the equation from log arrhythmic to exponential form . L | |
| 01:22 | N X means the natural log of X , and | |
| 01:27 | a natural log has a base of E . So | |
| 01:32 | converting the equation to exponential form , we have E | |
| 01:38 | to the eighth equals X squared next . Since X | |
| 01:43 | is squared , we take the square root of both | |
| 01:46 | sides on the right . The square root of x | |
| 01:49 | squared is X on the left . However , there | |
| 01:54 | are a couple things to watch out for first . | |
| 01:58 | Remember that the square root of E to the eighth | |
| 02:01 | is the same thing as E to the eighth to | |
| 02:04 | the one half , which simplifies to E to the | |
| 02:08 | eight times one half or eat to the fourth . | |
| 02:13 | Also remember that when we take the square root of | |
| 02:16 | both sides of an equation we use plus or minus | |
| 02:20 | . So our final answer is plus or minus . | |
| 02:23 | E . To the fourth equals X . |
DESCRIPTION:
In this example, weâre asked to expand the given logarithmic expression, log base 3 of M squared N to the 5th. Remember that our first law of logarithms states that if two values are multiplied together inside a logarithm, such as M squared times N to the 5th, then we can expand the logarithm into the sum of two separate logarithms, in this case log base 3 of M squared plus log base 3 of N to the 5th. Next, notice that each logarithm has a power inside the logarithm, and remember that our third law of logarithms states that if we have a power inside a logarithm, we can move the exponent to the front of the logarithm, so we have 2 times log base 3 of M + 5 times log base 3 of N.
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