SOLUTION: solve the logarithmic equation symbolically. ln2x+ln9x=ln19

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Question 542381: solve the logarithmic equation symbolically.
ln2x+ln9x=ln19
Answer by jpg7n16(66) About Me  (Show Source):
You can put this solution on YOUR website!
Since we know that
ln%28a%29%2Bln%28b%29=ln%28a%2Ab%29
we can then prove that
ln%282x%29%2Bln%289x%29=ln%282x%2A9x%29=ln%2818x%5E2%29
Also, since we know that if ln%28a%29=ln%28b%29, then a=b.
We can also prove that if
ln%2818x%5E2%29=ln%2819%29 then
18x%5E2=19
To solve for x:
x%5E2=19%2F18
x=sqrt%2819%2F18%29 or x=-sqrt%2819%2F18%29