# How do you solve #log (x+9) - log x = 1#?

##### 1 Answer

#### Explanation:

**1) Determine when the equation is defined**

First of all, let's determine for which

Any logarithmic expression is only defined if its argument is greater than

So, in your case,

As

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**2) Simplify the logarithmic equation**

As next, you should combine all your logarithmic expressions into one.

You can do this with the logarithmic law

Thus, you equation can be transformed as follows:

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**3) Eliminate the logarithmic term**

Now, as you haven't specified the base of the logarithm, I will assume that the base is

The inverse function of

Thus, to eliminate the logarithmic expression at the left side, you need to apply the function

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**4) Solve the equation**

... multiply both sides with

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**5) Check if the result is valid**

We need to check if our result

Here, this is the case, thus we can accept