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$35-44$ Logarithmic Equations Use the definition of the logarithmic function to find $x .$$${ (a)} \log _{2}\left(\frac{1}{2}\right)=x \quad \text { (b) } \log _{10} x=-3$$

a. $x=-1$b. $\frac{1}{1000}$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Campbell University

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

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$35-44$ Logarithmic Equati…

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Logarithmic Equations Use …

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Use a property of logarith…

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In Exercises $41-58,$ solv…

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Logarithmic Form Express t…

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$25-32$ Use the definition…

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 let's look at look to the base off to ah, half equal to x. So what is the by CIA? The two is the base. The X is the exponents and that is all equal to ah Hoff. Now Ah, half I can rewrite as to to the bar off Negative one. Now I can see because the basis or the same X is equal to negative one in the next one, we it's look to the bys often x equal to negative three. The thing is, the base, it's the base off the log So it becomes the base off the exponents with my exponents as negative three and this all equal to the extinct. Right? So this simply fires into X equal to zero comma 001 Or you can also write s one over 1000.

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