What is the value of $x$ in $222^x−111^x∗7=111^x$? Can anyone help me on this? It is for a 8th grader.

What is the value of $x$ in $222^x-111^x*7=111^x$?

I know the equation can be rearranged as $222^x=111^x*7-111^x=6*111^x$. Then what is next?

Set
$$111 = a$$
hence
$$222 = 2a$$
Now your equation is simpler:
$$(2a)^x -7 a^x = a^x$$
hence
$$(2a)^x = 8a^x$$
$$2^xa^x = 8a^x$$
Since the exponential is never zero (and here $a = 111$) divide by $a^x$
$$2^x = 8$$
Hence with the logarithm base $2$:
$$\lg(2^x) = \lg(8)$$
$$x = 3$$
