Logs in calculus

Question

I have this problem that according to the book, the steps do not come up to the answer which is 24. I hope someone can help me with this. Thank you.

Log4 ^x - log 4 ^(x-18) = 1   Solve for x.

Answer 1

Log₄ x  -  Log₄ (x - 18) = 1

Log₄ x / ( x - 18 )  = 1

Exponentiate both sides as a power of  4

Then the Inverse Rule  x = a ^ (log_a x ) applies with a = 4

x / ( x - 18 ) = 4

x = 4 ( x - 18 )

x = 4x - 72

3x = 72 

x = 24

 

Answer 2

Maybe you meant

log₄ x - log₄(x-18) = 1 ???????

 

If this is your equation, you get

 

log₄ x/(x-18) = 1

x/(x-18) = 4¹

x = 4x-72

-3x = -72

x=24

 

At least this works out to a nice answer, but I'm not sure if this is your actual equation. 

It is possible, as suggested in the comment  by Sava, that and equation has no solution.

 

Hope this helped