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$35-44$ Logarithmic Equations Use the definition …

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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 40 Medium Difficulty

$35-44$ Logarithmic Equations Use the definition of the logarithmic function to find $x .$
$${ (a)} \log _{4} 2=x \quad \text { (b) } \log _{4} x=2$$

Answer

a) $x=\frac{1}{2} \quad, \quad$ b) $x=16$

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Video Transcript

before we onto this question. Let's just recap on the definition off the logarithmic function. So if I have locked to the base off a be equal to see to rewrite this into exponential for I have the base off a to the power off, see equal to be right. So remember the base off the log becomes the base off the exponential form and then the sea becomes the exponents and the B is on the other side of the equal sign. Another thing is that you will remember that Lin off are you is the lock with base e off I great. So applying this to lock base for two equal to X We now have that full Easter base X is in the exponents and that is all equal to two. But remember, we are looking for the same base now to solve for X So I'm going to really like the to as the square root off four which in its own turn is four to the power off Ah half because the basis all the same now X is equal to 1/2 where we have locked to the base off four x equal to two again. Four is our base to is the exponents now on that is all equal to X, so this simply Farr's two x equal to 16.

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