$${log}_{10}\left({{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}\right) = {log}_{10}\left({\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}\right)$$
+23246 Since both logs are to the base 10, take both sides of the equation to the power of 10:
10log10 (x^2 - 2x ) = 10log10 (2x + 12)
Since 10log10 (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!
+23246 Since both logs are to the base 10, take both sides of the equation to the power of 10:
10log10 (x^2 - 2x ) = 10log10 (2x + 12)
Since 10log10 (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!
