Multiplying Scientific Notation | MathHelp.com - By MathHelp.com
00:0-1 | to multiply numbers that are written in scientific notation Such | |
00:04 | as 1.4 times 10 to the negative second Times 5.3 | |
00:10 | times 10 to the 6th . We first multiply the | |
00:13 | decimals in this case 1.4 times 5.3 to get 7.42 | |
00:21 | . Next we multiply the powers of 10 In this | |
00:24 | case 10 to the negative 2nd times 10 to the | |
00:27 | 6th . Notice that we're multiplying two powers that have | |
00:32 | like bases . So we add the exponents and leave | |
00:36 | the base the same to get 10 to the negative | |
00:40 | two plus six or 10 to the fourth . So | |
00:44 | we have 7.42 times 10 to the fourth . Finally | |
00:50 | , were asked to write our answer in scientific notation | |
00:54 | . Notice however that 7.4 , 2 times 10 to | |
00:58 | the negative fourth is already written in scientific notation Because | |
01:03 | we have a decimal between one and 10 That is | |
01:07 | multiplied by a power of 10 . So we have | |
01:10 | our answer . |
DESCRIPTION:
In this example, which involves natural logarithms, weâre asked to solve each of the following equations for x, and leave our answers in terms of e. To solve for x in the first equation, ln x = 3, we simply switch the equation from logarithmic to exponential form. Remember that ln x means the natural logarithm of x, and a natural log has a base of e. So, to convert the given equation to exponential form, remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have eâ¦to the 3rdâ¦= x, and weâve solved for x. Notice that our answer, e cubed, is written in terms of e, which is what the problem asks us to do. Now, letâs take a look at the second equation, ln x squared = 8. Again, we solve for x by switching the equation from logarithmic to exponential form. Ln x squared means the natural logarithm of x squared, and a natural log has a base of e. So, converting the equation to exponential form, we have eâ¦to the 8thâ¦= x squared. Next, since x is squared, we take the square root of both sides. On the right, the square root of x squared is x. On the left, however, there are a couple of things to watch out for. First, remember that the square root of e to the 8th is the same thing as e to the 8th to the ½, which simplifies to e to the 8 times ½, or e to the 4th. Also, remember that when we take the square root of both sides of an equation, we use plus or minus, so our final answer is plus or minus e to the 4th = x.
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