Question 42666
For the first problem, do you mean {{{sqrt(7)^(x+4)=49^x}}}?
If so it can be solved easily.  As written it is ambiguous and other ways to interpret it would make it harder to solve.
Note that {{{sqrt(7) = 7^(1/2)}}} and {{{49 = 7^2}}}.  We could rewrite the problem as {{{7^((x+4)/2)=7^(2x)}}}, so {{{(x+4)/2=2x}}}, leading to {{{x = 4/3}}}
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Second problem: 

{{{ln 2x + ln 8x = ln 17}}}
{{{ln 2 +ln x + ln 8 + ln x = ln 17}}}
{{{2*ln x = ln 17 - ln 2 - ln 8}}}
{{{ln x^2 = ln (17/(2*8)) }}}
{{{x^2 = 17/16}}}
{{{x = sqrt(17)/4}}}