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To solve a logarithmic equation, rewrite the equation in exponential form and solve for the variable.
Let both sides be exponents of the base e. 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.
The equation can now be written Step 3: The exact answer is and the approximate answer is Check: You can check your answer in two ways. You could graph the function Ln x -8 and see where it crosses the x-axis. If you are correct, the graph should cross the x-axis at the answer you derived algebraically.
You can also check your answer by substituting the value of x in the initial equation and determine whether the left side equals the right side. For example, if Ln 2, It does, and you are correct. Isolate the logarithmic term before you convert the logarithmic equation to an exponential equation.
Divide both sides of the original equation by 7: Convert the logarithmic equation to an exponential equation: If no base is indicated, it means the base of the logarithm is Recall also that logarithms are exponents, so the exponent is.
The equation Step 3: Divide both sides of the above equation by 3: You can check your answer in two ways: If you choose graphing, the x-intercept should be the same as the answer you derived.
If you choose substitution, the value of the left side of the original equation should equal the value of the right side of the equation after you have calculated the value of each side based on your answer for x.
Solve for x in the equation Solution: If we require that x be any real number greater than 3, all three terms will be valid. If all three terms are valid, then the equation is valid. Simplify the left side of the above equation: By the properties of logarithms, we know that Step 3: The equation can now be written Step 4: Let each side of the above equation be the exponent of the base e: Simplify the above equation: In the case of this problem, then Step 6: Factor the left side of the above equation: If the product of two factors equals zero, at least one of the factor has to be zero.
Why is 9 the only solution? We defined our domain to be all the real numbers greater than 3. You can check your answer by graphing the function and determining whether the x-intercept is also equal to 9.
If it is, you have worked the problem correctly. You could also check your answer by substituting 9 for x in the left and right sides of the original equation.
If, after the substitution, the left side of the equation has the same value as the right side of the equation, you have worked the problem correctly.How Do You Evaluate a Logarithm?
If you want to solve a logarithm, you can rewrite it in exponential form and solve it that way! Follow along with this tutorial to practice solving a logarithm by first converting it to exponential form.
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. Mar 28, · Writing exponential equations into logarithmic form? RE: Writing exponential equations into logarithmic form?
How do I write this equation in Logarithmic form?
More questions. Exponential and logarithmic expressions and equations? Logarithmic equations with a negative?Status: Resolved. 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. Find the logarithm of to the base Remember that the domain of the logarithm is `(0,oo)`, so if you enter the value outside of this interval, the result will be a complex number.
If you enter negative base, the result will be a complex number. Examples of How to Find the Inverse of a Logarithm. Example 1: Find the inverse of the log equation Start by replacing the function notation f (x) by webkandii.com, interchange the roles of x and y..
Proceed by solving for “ y ” and replacing it by f -1 (x) to get the inverse. Part of the solution below includes rewriting the log equation into an exponential equation.