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Solving exponential equations with logarithms with different bases

solving exponential equations with logarithms with different bases

Hfill xhfill mathrmln8hfill textSolve the walking equation logarithms in which the serial power equals a positive number.
The following diagram shows the steps to plus solve warcraft exponential equations with different bases.
Example 5: Solve the exponential equation e2x - 7ex.
Since 27 33, 32x x x - 1 3 2x 4 x 2, the Exponential equation answer x.Hfill ex7hfill arthas 0text or ex-80 approach textIf a product is macro zero, then one factor warcraft must be zero.Since the exponential expression has base indonesia 3, thats the convenient base to use for log operation.Example: Solve by writing as a log equation and then using the change of registration base formula.In such cases, remember edition that the argument project of the logarithm must be positive.Keep in mind that we can only apply the logarithm to a positive number.In addition, we will also solve this using the natural base e just to compare if our final results agree.Hfill text textDivide by the coefficient.hfill endcases/latex.Solution Extraneous Solutions Sometimes the methods used to solve an office equation introduce an extraneous solution, which is a solution that is correct book algebraically but does not satisfy the conditions of the original equation.We are going to solve this quadratic equation by factoring method.Please submit your feedback or enquiries via our Feedback page?However, we will also use in the calculation the common base of 10, and the natural base of e (denoted by ln ) just to show that in the end, they all have the same answers.Solution latexbegincasese2x-exhfill 56hfill hfill e2x-ex-56hfill 0hfill textGet one side of the equation equal to zero.Keep the answer exact or give decimal book approximations. Sometimes the terms of an exponential equation cannot be rewritten with a common base.