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Solving Exponential Equations

Recall that the inverse of an exponential function is a logarithmic function. We can use the natural logarithm, ln x, to solve an exponential equation. The following property of  logarithms will be needed,

, for any real number k and any positive number u.

Example

Solve the equation  for x.

Solution

We first divide both sides by 1.5,

                                                             .

Now take the natural logarithm of both sides and apply logarithm property 3,