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$35-44$ Logarithmic Equations Use the definition of the logarithmic function to find $x .$$${ (a)} \log _{x} 16=4 \quad \text { (b) } \log _{x} 8=\frac{3}{2}$$
a) $x=2 \quad, \quad$ b) $x=4$
Algebra
Chapter 4
Exponential and Logarithmic Functions
Section 3
Logarithmic Functions
Oregon State University
Baylor University
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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. So let's apply this to log off base X 16 equal to full. Sorry, this guy's exist. The base off off the lock so it will become the base off the exponents way four is the experiment. And this is in the exponential for all equal to 16 now, 16. Aiken relied as to to the power off four. So taking the fourth fruit on both sides. I get aches equal to two. Right. Then at B full log aches right equal to 3/2. I have the base off aches the exponents off three over to all equal to eight. So what I'm going to do here now to get rid of the 3/2, I'm going to our both sides to to over three. So on the left hand side, the threes will cancel out. So the two fractions will cancel out and I have lived. X is equal to now. Eight to the power off. Two of three is equal to four.
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