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$9-16$ Exponential Form Express the equation in e…

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Problem 1 Problem 2 Problem 3 Problem 4 Problem 5 Problem 6 Problem 7 Problem 8 Problem 9 Problem 10 Problem 11 Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 Problem 17 Problem 18 Problem 19 Problem 20 Problem 21 Problem 22 Problem 23 Problem 24 Problem 25 Problem 26 Problem 27 Problem 28 Problem 29 Problem 30 Problem 31 Problem 32 Problem 33 Problem 34 Problem 35 Problem 36 Problem 37 Problem 38 Problem 39 Problem 40 Problem 41 Problem 42 Problem 43 Problem 44 Problem 45 Problem 46 Problem 47 Problem 48 Problem 49 Problem 50 Problem 51 Problem 52 Problem 53 Problem 54 Problem 55 Problem 56 Problem 57 Problem 58 Problem 59 Problem 60 Problem 61 Problem 62 Problem 63 Problem 64 Problem 65 Problem 66 Problem 67 Problem 68 Problem 69 Problem 70 Problem 71 Problem 72 Problem 73 Problem 74 Problem 75 Problem 76 Problem 77 Problem 78 Problem 79 Problem 80 Problem 81 Problem 82 Problem 83 Problem 84 Problem 85 Problem 86 Problem 87 Problem 88 Problem 89 Problem 90 Problem 91 Problem 92 Problem 93 Problem 94 Problem 95 Problem 96 Problem 97 Problem 98 Problem 99 Problem 100 Problem 101 Problem 102 Problem 103 Problem 104 Problem 105

Problem 10 Medium Difficulty

Express the equation in exponential form.
(a) $\log _{5}\left(\frac{1}{5}\right)=-1$
(b) $\log _{4} 64=3$

Answer

$$
\begin{array}{l}{\text { a. } 5^{-1}=\frac{1}{5}} \\ {\text { b. } 4^{3}=64}\end{array}
$$

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Video Transcript

for this exercise. We want to express the equation and exponential form for part A were given the log rhythmic equation. Log base five off 1/5 is equal to negative one. Our log rhythmic rule states that if we have the log base B of A is equal to X. That is equivalent to be raised to the X. Power is equal to a so to convert from log rhythmic form exponential form, you would take your base and raise it to the value that is on the opposite side of your equation. So for our example, let's go back. Um, I've got my base, which is five, and I want to raise that to the negative one power. So my answer would be five to the negative one. Power is equal to 1/5. So now let's take a look at part B. We have the log. These four of 64 is equal to three. So my log rhythmic rule states that I take my base, which is four, and raise that to my opposite side of my equation, which would be three Oh, so I would have four raised to the third. Power is equal to 64 is my exponential, um, expression. So also, you can always go back and check to make sure you've gotten it correct. If I take four to the third power, that's four times itself three times, which would be equal to 64 So I know I have the

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