The first thing we can do is get rid of the exponent in the second log, and then divide both sides by that coefficient:

It can be a pain to work with logs of different bases, so let's change the base  log to base :

We can now take the denominator, expand, and simplify:

Now, we combine the log terms:

Taking the square root of each side:

We have to solve for both the plus, and the minus.  Let's start with the negative:

And now the positive:

Plugging both of these answers into the original equation produces no errors, so both answers are valid.

First, we can use the log product rule to combine the log terms:

Now we write the equation in exponential form:

If we plug  into the original equation, we get errors (we can't take the log of a negative value).   is fine though, and is our only solution.

We can combine the logs on the right side of the equation while also using the product rule on the log on the left side:

Since the logs have the same base, we can equate the algebraic equations equal to each other:

Now we can solve the quadratic equation:

Plugging this into the original equation doesn't produce errors, so it's our single solution.

First we take the natural log of both sides of the equation:

Remember, taking the natural log of  with an exponent equals that exponent, and the natural log of  is :

Form here, we solve algebraically:

First we start by subtracting  from each side:

Next, we rewrite the equation in exponent form:

Finally, we divide by :

First, we subtract  from each side:

Next, we divide each side by :

Now we rewrite the equation in exponent form:

And we finish using algebra:

First, we add  to each side:

Next, we take the exponent in the log and make it a coefficient:

And divide by the new coefficient:

Now we write the equation in exponent form:

The first thing we can do is combine all the log terms on the right side of the equation:

Next, we can take the coefficient from the left term and make it an exponent:

Now we can cancel the logs from both sides:

When we put  back into the original question, we don't have problems.  When we try it with  however, we get errors, so that's not a valid answer:

First, we take the coefficient, , and make it an exponent:

Now we can cancel the logs:

When we check our answers, however, we notice that  results in errors, so that's not a valid answer:

First, we combine the log terms on the left of the equation:

Now we can cancel the logs on each side:

We can subtract  from each side to set the equation equal to .  this will give us a nice quadratic equation to solve:

Notice that  is not a valid answer, because if we plug it into the original equation then we would be taking the log of a negative number, which we can't do.  Our only solution is: