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For the following exercises, use the change-of-base formula to evaluate each expression as a quotient of natural logs. Use a calculator to approximate each to five decimal places.$$\log _{\frac{1}{2}}(4.7)$$
426.8
Algebra
Chapter 6
Exponential and Logarithmic Functions
Section 5
Logarithmic Properties
Functions
Oregon State University
McMaster University
Harvey Mudd College
University of Michigan - Ann Arbor
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number 2 85 So we have a lager with Mick expression that is currently based 1/2 and we're going to change the expression to base e using the change of based formula. So notice in our expression the current base is 1/2 and that's represented by a bee in the formula and that be when we change, the base is going to be over. Here is the argument of the log and the denominator and then notice back in our problem. We have 4.7 as our argument, and that's represented with an M in the formula. And that's gonna be the argument of the top blogger rhythm in the formula. And then we're changing it to base e So n is E. And we don't say log Basie. We just say natural log. So putting all that together, we get the natural log of 4.7 over the natural log of 1/2 and then we could put that into our calculators and we get approximately negative 2.23 to 66
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