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Ron-Jon commits an error when he simplifies the expression $(g(x))_{10}$ to $x,$ since they are not equivalent. He has raised to $10$

instead of $10$ raised to the power of

. This cannot be simplified to $x,$ but just means to take the $g(x)$ multiplied by itself $10$ times.
$(g(x))_{10}=10g(x)⋅g(x)⋅…⋅g(x) $

b

In order to get $x$ alone, he should have used that the common logarithm and a power with the base $10$ undo each other. $10_{log(x)}=x$ This is a rule also known as an inverse property of logarithms. Now, let's solve it correctly!