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:

The first thing we can do is move both log functions to one side of the equation:

Then we can combine the log functions (remember, when you add logs, we multiply the terms inside):

Now we can rewrite the equation in exponent form (and FOIL the multiplied terms):

We can collect all the terms on one side of the equation, and then solve the quadratic:

However, if we plug  into the initial equation, we would be taking the log of a negative number, which we can't do, so it's not a valid solution:

We first put both logs on one side of the equation:

Now we combine the log terms (remember, when we subtract logs we divide the terms inside):

We can now rewrite the equation in exponential form:

Anything raised to the  power is , and now we can solve algebraically:

We start by rewriting the equation in exponential form:

Now we can simplify:

We can either do this the long and proper way, or the simple and easy way.

The long way:

First, we move both logs to the same side of the equation:

Now we can combine the logs (reminder, when you subtract logs, you divide the terms inside of them):

Let's rewrite the equation in exponential form:

Anything raised to the  power equals , so we can simplify and solve from here:

The short way:

First, we cancel the log terms (because the base is the same, and all we have are the log terms):

Then we divide by :