What is the solution for log equations with a base of 4 and a difference of 3?

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Homework Help Overview

The discussion revolves around solving a logarithmic equation involving a base of 4, specifically the equation log4 x - log4 (x-3) = 5. Participants are exploring the implications of logarithmic properties and algebraic manipulation.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants attempt to manipulate the logarithmic equation into a more solvable form, questioning the steps needed to isolate x. There are discussions about the implications of the logarithmic properties and the algebraic steps involved in solving for x.

Discussion Status

The discussion is ongoing, with participants providing guidance on algebraic manipulation and questioning the validity of solutions. There is a focus on ensuring that the solutions meet the conditions required for logarithmic functions.

Contextual Notes

Participants are grappling with the algebraic steps necessary to solve for x and the conditions that must be satisfied for the logarithmic expressions to be valid, particularly the requirement that x must be greater than 3.

  • #31


Mentallic said:
Not quite, 3*1023=3069

starting over, this is how i work it

log4 x/x-3 = 5

x/x-3 = 4^5

x = 1024 (x-3)

x = 1024x - 3072

x - 1024x = -3072

1023x = -3072

1023x/1023 = -3072/1023

x = -3.003
 
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  • #32


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?
 
  • #33


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?

divide it by 1023
 
  • #34


Now solve for x.
 
  • #35


BloodyFrozen said:
Now solve for x.

x=3.003
 

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