How do you solve #2-6lnx=10#?

1 Answer
SCooke
Aug 10, 2017

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

Explanation:

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

# 2 − 6xxln(x) = 10# ; #-6ln(x) = 8# ; #ln(x) = -(4/3)#

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

#e^(ln(x)) = e^(-(4/3))# ; # x = 0.264#

CHECK:
# 2 − 6xxln(x) = 10# ; # 2 − 6ln(0.264) = 10#

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

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