How do you solve $2 - 6 ln x = 10$ $2-6lnx=10$ ?

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Answer 1 · 2017-08-10T12:57:32

Work it like a normal algebra problem to get ln x on one side. Then use a calculator or log tables.

Until you get to the actual logarithm the math is the same as for any algebra equation.

$2 - 6 \times ln (x) = 10$ $2 − 6xxln(x) = 10$ ; $- 6 ln (x) = 8$ $-6ln(x) = 8$ ; $ln (x) = - (\frac{4}{3})$ $ln(x) = -(4/3)$

NOW we take the antilog, inverse, or exponential of both sides:

$e^{ln (x)} = e^{- (\frac{4}{3})}$ $e^(ln(x)) = e^(-(4/3))$ ; $x = 0.264$ $x = 0.264$

CHECK:
$2 - 6 \times ln (x) = 10$ $2 − 6xxln(x) = 10$ ; $2 - 6 ln (0.264) = 10$ $2 − 6ln(0.264) = 10$

$2 - 6 (- 1.33) = 10$ $2 − 6(-1.33) = 10$ ; $2 - (- 8) = 10$ $2 - (-8) = 10$ ; $10 = 10$ $10 = 10$ CORRECT!

How do you solve 2−6lnx=102-6lnx=10?