How do I solve this algebraically?
2-6lnx= 10

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

−

6

×

ln

(

x

)

=

10

;  

−

6

ln

(

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

−

6

×

ln

(

x

)

=

10

;  

2

−

6

ln

(

0.264

)

=

10

2

−

6

(

−

1.33

)

=

10

;  

2

−

(

−

8

)

=

10

;  

10

=

10

CORRECT!