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$35-44$ Logarithmic Equations Use the definition of the logarithmic function to find $x .$$${ (a)} \log _{7}\left(\frac{1}{49}\right)=x \quad \text { (b) } \log _{2} x=5$$
a.$y=-2$b. $x=32$
Algebra
Chapter 4
Exponential and Logarithmic Functions
Section 3
Logarithmic Functions
Harvey Mudd College
University of Michigan - Ann Arbor
Lectures
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$35-44$ Logarithmic Equati…
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Use a property of logarith…
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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. Let's see how this applies to lock off by seven 1/49 equal to eggs. So what is the by CIA? This same unease The base, the eggs is the exponents and that will all be equal to 1/49. Now, remember, 49 in the denominator, I can write us writers 49 to the bar of negative one to get into the numerator. And now I'm looking for the same base for these two in the equation. And I see that 49 is Sevan squid and I just apply the negative one. They s again. So now seven to the bar off eggs is equal to see even to the boat off. Negative too. On this thing because the basis all the same X is equal to negative too. In look to the base off two X equal to five. Choose the base five first the exponents and that is all equal to X. Simplifying this, it leaves us with X equal to 32.
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