Evaluating logs11/4/2022 ![]() Step 8: Factor the left side of the above equation: Step 6: Simplify the left side of the above equation: Step 4: Let each side of the above equation be the exponent of the base e:Īnother way of looking at the equation in Step 3 is to realize that if Ln( a) Step 2: Simplify the left side of the above equation: By the properties of logarithms, we know that ![]() If all three terms are valid, then the equation is valid. If we require that x be any real number greater than 3, all three terms will be valid. Solution: Step 1: Note the first term Ln( x-3) is valid only when x>3 the term Ln( x-2) is valid only when x>2 and the term Ln(2 x+24) is valid only when x>-12. Have calculated the value of each side based on your answer for x. If you choose substitution, the value of the left side of the originalĮquation should equal the value of the right side of the equation after you If you choose graphing, the x-intercept should be the same as the answer you Or substituting the value of x into the original equation. Is the exact answer and is the approximate answer.Ĭheck: You can check your answer in two ways: graphing the function Step 3: Divide both sides of the above equation by 3: Recall also that logarithms are exponents, so the exponent is Step 2: Convert the logarithmic equation to an exponential equation: If no base is indicated, it means the base of the logarithm is 10. Divide both sides of the original equation by 7: Solution: Step 1: Isolate the logarithmic term before you convert the logarithmic equation to an exponential equation. It does, and you are correct.Įxample 2: Solve for x in the equation 7 Log(3 x)=15. You can also check your answer by substituting the value of x in the initialĮquation and determine whether the left side equals the right side. ![]() If you are correct, the graph should cross the x-axis at the answer you derived algebraically. ![]() You could graph the function Ln( x)-8 and see where it crosses the x-axis. The equation can now be writtenĬheck: You can check your answer in two ways. Step 2: By now you should know that when the base of the exponent and the base of the logarithm are the same, the left side can be written x. Solution: Step 1: Let both sides be exponents of the base e. To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.Įxample 1: Solve for x in the equation Ln( x)=8. ![]()
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