Question 64622
The first step is to get everything into the same base logarithm, by using the formula {{{log (10,x) = (ln x)/(ln 10) }}}.


log(x) + ln(x) = 1
{{{(ln x)/(ln 10) +ln x = 1 }}}.


You might want to clear the fraction by multiplying both sides times ln 10:
{{{ln x + (ln 10)*(ln x) = ln 10}}}


Next, factor the ln x, which is a common factor on the left side:
{{{(ln x) *(1 + ln 10) = ln 10}}}


Divide both sides by (1 + ln 10)

{{{ln x = (ln 10)/(1+ ln 10) }}}


Raise both sides as a power of e:

{{{x = e^((ln 10)/(1+ ln 10)) }}}


R^2 at SCC   


P.S.  Nice problem!!!