# How do you solve? log(x-1) + log 2x= log2x^2 - log2

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**How do you solve**

**Please note:**It is assumed that an expression like log(x) means take the common logarithm, i.e. base 10 logarithm of x. If another base is intended, it should be indicated, as in# color(brown)( log_2 (x) # . or use# color(brown)( ln (x) # for the "natural, base e logarithm".

**Using properties of logarithms, we can combine terms, then rearrange terms to isolate x, if possible.** Also, **we must assume**

If two logarithm expressions with the same base are equal then the arguments of the functions are equal.

Simplify and solve for x.

Subtract

Either **which is not allowed**,

or

**We're not finished until we check**, since there may have been an error in the work, or the only possible solution may not work.

**YES!!!** We have our solution.

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