Question

Lg(10x+200)=lgalign="absmiddle" class="latex-formula">
+lg10​

Answer 1

Answer: x = {-4, 5}

Step-by-step explanation:

log (10x + 200) = log (x²) + log (10)

log (10x + 200) = log (10x²)

     10x + 200 = 10x²

                   0 = 10x² - 10x - 200

                   0 = x² - x - 20

                   0 = (x - 5)(x + 4)

                   0 = x - 5    0 = x + 4

                  x = 5           x = -4

Check for extraneous solutions:

             10x + 200 > 0                  x² > 0

x = 5      10(5) + 200 > 0               (5)² > 0        both are satisfied

x = -4     10(-4) + 200 > 0             (-4)² > 0        both are satisfied

            Both solutions are valid!