Now we factor (or use the Quadratic Formula). This is a quadratic equation so we want one side to be zero. To make this easier I am going to eliminate the fractions by multiplying by 10: Using this pattern on your equation we get: Now that we have the first form, the next step is to rewrite the equation in exponential form. Since your logarithms have a "+" between them, we willuse the first property: Your logarithms meet both of these requirements. Coefficients of 1 in front of the two logarithms.Your logarithms have the same base, 10, but different arguments, x+3/10 and x.įortunately there are two properties of logarithms which allow us to combine two logarithms into one: (Like logarithmic terms have the same bases and the same arguments. They are not like terms so we cannot just add them together. Now we need to find a way to combine the two logs into one. We want the "non-log" terms on one side and the log terms on the other so we will subtract 1 from each side: With the "non-log" terms of 1 and 0, the second form will be more difficult to achieve. Solving equations where the variable is in the argument of a logarithm usually starts with transforming the equation into one of the following forms: You can put this solution on YOUR website!
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