[SOUND] Let's look at some examples of solve logarithmic equations.

[SOUND] For example, let's solve this equation for x.

We can begin by bringing in the 8 to the right-hand side which would give us that

log base 5 of x + 4 = 9 - 8, or 1. And now writing this in exponential form

gives us that 5^1 = x + 4. Because remember that log base a of x = y

is equivalent to the exponential form a^y = x, which is what we used here.

And now, if we subtract 4 from both sides, we get that x = 5 - 4 or 1.

Now, in solving logarithmic equations, it's very important for us to check our

answers, so let's do that. Let's check that this value, x = 1, satisfies this

equation. Namely, is 8 + log5(1+4) = 9, or is 8 +

log5(5) = 9. And it is because log5(5) is 1, and 8 + 1

is 9, so yes, it works. Therefore, our answer is x = 1.

Alright, let's see another example. [SOUND] Let's solve this equation for x.

Now, we can begin here by condensing the left-hand side into a single logarithm by

using the following property. The logA + logB is equal to the log of

the product, A * B. That is, this equation is equivalent to

log(x-15) * x = 2. And now, we can convert this into

exponential form again by using this equivalence here, and remembering though

that log means log base 10. That is, this equation is equivalent to

10^2 = x-15 * x, or 100 is equal to, and now distributing our x we have x^2 - 15x.

And bringing all the terms to one side gives us that x^2 - 15x - 100 = 0.

And now, let's factor the left-hand side. It factors into (x-20) (x+5).