Exponential and Log Equations: Solve 3 ln 2+ ln (x-1) = ln 24

[Kathy0316]

3 ln 2+ ln (x-1) = ln 24

 

[ksdhart2]

What have you done? What have you tried? Please share with us any and all work you've done on this problem, even if you know it's wrong.

 

[impel tutors]

Answer

3 ln 2+ ln (x-1) = ln 24

ln 8 + ln (x-1) = ln 24

ln 8(x-1) = ln 24

8(x-1) = 24

x-1 = 3

x = 4

 

[Steven G]

3 ln 2+ ln (x-1) = ln 24

ln 8 + ln (x-1) = ln 24

ln 8(x-1) = ln 24

8(x-1) = 24

x-1 = 3

x = 4

Very nicely done. Now you need to check that all of the arguments are positive when x=4.

 

[stapel]

Solve 3 ln 2+ ln (x-1) = ln 24

i. Apply a log rule to move the multiplier on the first term on the left-hand side inside the log as an exponent. Simplify.

ii. Apply another log rule to combine the two logs on the left-hand side into one.

iii. The two log expressions are equal only if their insides are equal. Create the resulting linear equation.

iv. Solve the linear equation for the value of x.

v. Check that this value works in the original log equation.

If you get stuck, please reply showing your work in following the above steps. Thank you!