SOLUTION: how do you write the expression as a single logarithum: 1/2[log(base4)(x+1) + 2log(base4)(x-1)] +6log(base4)(x)

Question 174002: how do you write the expression as a single logarithum:
1/2[log(base4)(x+1) + 2log(base4)(x-1)] +6log(base4)(x)
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
your equation is:
1/2[log(base4)(x+1) + 2log(base4)(x-1)] +6log(base4)(x)
this looks to me like:

-----
you have a couple of concepts to work with:
these are:

-----
we will remove the inner parentheses first and work outwards.
you have:

this becomes:

-----
working our way outwards, you have:

this becomes:

working our way outwards again, you have:

this becomes:

we now have in total:

so we have:

and this becomes:

-----
i checked the answer and it appears to be good.
i did this by solving both equations for a given value of x.
i used x = 2.
i got the same answer both ways (the original equation and the condensed equation).
-----
you can solve this as well if you wish to prove the answer is good.
you can use your calculator by converting to base 10 as follows:

-----

RELATED QUESTIONS
Log base4 (x^2 - 3) + Lobg base4... (answered by Earlsdon)

Solve: 2log(base4)x+log(base4)3=log(base4)x-log(base4)2 (answered by rapaljer)

find the two values of x that satisfy the equation:... (answered by nerdybill,josmiceli)

Log(base4)(2x+1)=Log(base4)(x-3)+Log(base4)(x+5) (answered by Nate)

Use properties of logarithms to solve the equation log(base4)(x+2)=... (answered by ewatrrr)

(1/3)log(base4)*27-(2log(base4)*6-(1/2)log(base4)*81 (answered by lwsshak3)

log(base2)(log(base4)x)=1 (answered by Fombitz)

solve for x log(base4)(x^2-3x) =... (answered by josmiceli)

How do you solve log base4(x+2)... (answered by Alan3354)