When a logarithm equals , the equation in the logarithm equals the logarithms base:

First we start by subtracting from each side:

Next, we rewrite the equation in exponent form:

Finally, we divide by :

First we rewrite the equation in exponential form:

Now we take the cube root of :

First we subtract from both sides:

Then we divide both sides by :

Now it would help if we wrote the equation in exponential form (remember, if the log doesn't show a base, it's base 10):

Finally, we use algebra to solve:

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 rearrange the equation, trading the logarithm for an exponent:

And then we solve:

First, we can combine the log terms:

Now we can change to exponent form (remember, if a log doesn't specifically have a base, then it's base 10):

We need to set the equation equal to in order to solve the quadratic equation, so we combine the terms and subtract :

Then we factor and solve for :

Lastly, we have to check our answers. When we plug in to the original equation, everything comes out well. However, when we use we get errors (because you can't take the log of a negative number). Therefore, we only have 1 solution: .

In order to solve for the logs, we will need to write the log properties as follows:

and

This means that:

Replace the values into the expression.

The answer is:

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:

To solve for x, we must take the logarithm of both sides (common or natural, it doesn't matter):

In doing this, we can now bring the exponents in front of the logarithms:

Now, solve for x: