We begin with the following:

This can be rewritten as

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

Solve this to get t.

The first step is to make sure we don't have a zero on one side which we can easily take care of:

Now we can take the logarithm of both sides using natural log:

Note: we can apply the Power Rule here

Step 1: Rewrite the right side as a power of :

Step 2: Rewrite the original equation:

Step 3: Since the bases are equal, I can set the exponents equal.

So,

Before beginning to solve for , we need to have a coefficient of :

Now we can take the natural log of both sides:

Note:

Isolate the variable by dividing by 6.

is the same as .

We begin with the following:

This can be rewritten as

Recall that if you have two exponents with equal bases, you can simply set the exponents equal to eachother. Do so to get the following:

Solve this to get t.

To solve, use the natural .

Step 1: Rewrite the right hand side of the equation as a power of 2.

. To get this, divide the base by 2 and multiply that 2 to the exponent...

Step 2: Equate the left and right side together

We have the same base, so we equate the exponents together..

...

Isolate by adding to both sides of the exponential equation.

Take the common log.

Use logarithmic rule 3. An exponent inside a log can be moved outside as a multiplier.

Simplify. Because

Isolate the variable by subtracting from both sides.

Step 1: Write as ...

Step 2: Rewrite as in the original equation..

Step 3: By a rule of exponents, I can set the exponents equal if the bases of both exponents are the same...

So,