Log10X=LnX Solve for X

the 10 is small subscript by the way.

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Note:
Let log denote common logarithm
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                      log(x) = ln(x)
                      log(x) = log(x)/log(e)            ← By logarithm conversion rule
log(x) - log(x)/log(e) = 0                       ← Now, factor
log(x)[1 - (1/log(e))] = 0

possible solutions are for:
➊ log(x) = 0
             x = 10⁰
             x = 1 ✔        ← substituting this into the original equation shows that it works

➋ 1 - (1/log(e)) = 0        ← There is no x in this equation.
                                            So, there can be no solution for x here.



     From ➊ & ➋ we have:
              ANSWER
                  x = 1


Have a good one!
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log x = ln x = logx/loge ==> log e = 1 ! not true...this is an imposible equality