For the equation ae^ct=d, solve for the variable t in terms of a, c, and d. Express your answer in terms of the natural logarithm.

We have the equation:

And we want to solve it for t, we will get:

Remember the rule:

and the rule:

Then we can apply the natural logarithm to both sides to get:

Now we use the second rule and then the first rule to get:

This is the solution we wanted.

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We have been given an equation . We are asked to solve the equation for t.

First of all, we will divide both sides of equation by a.

Now we will take natural log on both sides.

Using natural log property , we will get:

We know that , so we will get:

Now we will divide both sides by c as:

Therefore, our solution would be .