The solution to the logarithmic equation log4 x - log4 (x-3) = 5 is derived through algebraic manipulation. By applying the properties of logarithms, the equation simplifies to x/(x-3) = 45, leading to x/(x-3) = 1024. Further simplification results in the equation 1023x = 3072, yielding the final solution x = 3.003. It is crucial to verify that the solution satisfies the conditions x > 0 and x - 3 > 0.
PREREQUISITESStudents studying algebra, particularly those struggling with logarithmic equations, as well as educators looking for examples of logarithmic problem-solving techniques.
Mentallic said:Not quite, 3*1023=3069
HallsofIvy said:Yes, that is correct- only one step left.
You have 1023x= 3072 and you want x= something. How do you get rid of the "1023" that is multiplying the x?
BloodyFrozen said:Now solve for x.