How to Solve a Logarithmic Equation on a Given Base?

[colt]

Homework Statement

solve the log x²-4x-5 on the base x-2.[/B]

Homework Equations

I read a comment from someone that also saw the question that says:

making the equation equal to zero, the x values became approximately: 5.1623 and -1.1623

The Attempt at a Solution

If it was x²-4x+4, that would be igual (x-2)² and the answer would be 2, but I have no idea the guy got these broken numbers. Making what equal to zero?
the x²-4x-5? Doesn't make sense.

 

[SammyS]

Homework Statement

[/B].

solve the log x²-4x-5 on the base x-2.

Homework Equations

I read a comment from someone that also saw the question that says:

making the equation equal to zero, the x values became approximately: 5.1623 and -1.1623

The Attempt at a Solution

If it was x²-4x+4, that would be igual (x-2)² and the answer would be 2, but I have no idea the guy got these broken numbers. Making what equal to zero?
the x²-4x-5? Doesn't make sense.

First of all: There is no equation to be solved in your thread.

Second: x² − 4x − 5 can be factored quite nicely.

Third: What do you mean by " base x-2 " ?

Added in Edit:

Fourth: x = 5.1623 , −1.1623 are approximate solutions to x² − 4x − 6 = 0 .

 

[haruspex]

Where does the question come from?

 

[colt]

First of all: There is no equation to be solved in your thread.
Third: What do you mean by " base x-2 " ?

It's the base of the log, $(x-2) ^ {y} = x² -4x -5$. The statement is to solve it.

Where does the question come from?

From a video where the presenter receives random questions about several subjects. Someone asked it, a comment about it mentioned the roots and I got curious about whether this has a solution or not.

 

[haruspex]

It's the base of the log, $(x-2) ^ {y} = x² -4x -5$. The statement is to solve it.
From a video where the presenter receives random questions about several subjects. Someone asked it, a comment about it mentioned the roots and I got curious about whether this has a solution or not.

Ok, so we should not be too surprised that the question makes no sense.