Properties 3 and 4 leads to a nice relationship between the logarithm and exponential function. This is a nice fact to remember on occasion. We will be looking at this property in detail in a couple of sections.
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Solving Logarithm Equations In this section we will now take a look at solving logarithmic equations, or equations with logarithms in them.
We will be looking at two specific types of equations here. In particular we will look at equations in which every term is a logarithm and we also look at equations in which all but one term in the equation is a logarithm and the term without the logarithm will be a constant.
Also, we will be assuming that the logarithms in each equation will have the same base. If there is more than one base in the logarithms in the equation the solution process becomes much more difficult. Before we get into the solution process we will need to remember that we can only plug positive numbers into a logarithm.
Example 1 Solve each of the following equations. We will also need to deal with the coefficient in front of the first term. So, we saw how to do this kind of work in a set of examples in the previous section so we just need to do the same thing here. We are excluding it because once we plug it into the original equation we end up with logarithms of negative numbers.
It is possible for positive numbers to not be solutions. There is no reason to expect to always have to throw one of the two out as a solution. In order to solve these kinds of equations we will need to remember the exponential form of the logarithm.
Example 2 Solve each of the following equations. We need a single log in the equation with a coefficient of one and a constant on the other side of the equal sign. Once we have the equation in this form we simply convert to exponential form.
Here is the exponential form of this equation.in logarithmic form. In this example, the base is 7 and the base moved from the right side of the exponential equation to the left side of the logarithmic equation and the word “log” was added.
Example 5: Write the exponential equation 37 = y 5 in logarithmic form. Rewrite each equation in exponential form. 1) log 2) log 3) log 4) log Rewrite each equation in logarithmic form. 5) log 6) log 7) log 8) log Rewrite each equation in exponential form.
9) log x y xy 10) log n n 11) log x. 1 Rewriting Exponential and Logarithmic equations When solving an exponential or logarithmic equation, the rst step is to rewrite the equation so that the unknown is isolated on one side.
To do this we use all the mad skillz we have been developing in rewriting equations. 1. 7x = 14 x = log 7 14 2. y4 = y = y = 4 3.
log 9 d = 3 d = Example 1: Method #1 (Take the “log” of each side of the equation) 2 x = 7 take the log of each side of the equation log2 x = log7 solve the logarithmic equation This preview has intentionally blurred sections.
Start studying Rewrite Logarithmic Equations as Exponential Equations. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Jun 16, · Rewrite the logarithmic equation in the exponential form.?
Please Help!!! rewrite the following as a logarithmic equation: b^y= x? More questions. Rewrite as a Logarithmic equations? Rewrite as a logarithmic equation 3^-2 = 1/9? Answer Questions. Solving a Status: Resolved.