logarithm equation

Since both logs are to the base 10, take both sides of the equation to the power of 10:

10^{log₁₀ (x^2 - 2x} )  =  10^{log₁₀ (2x + 12)}

Since 10^log₁₀ (Anything)  =  Anything

--->   x² - 2x  =  2x + 12

--->   x² - 4x - 12  =  0

--->   (x - 6)(x + 2)  =  0

--->   x = 6  or  x = -2

In problems like these, you need to check all the answers; they do work!

Could you just cross out the log₁₀ from both sides? -- So long as all of both sides are in log form, yes!

Someone? please