SOLUTION: I need help solving these problems. {{{ 2log(3,x)-log(3,x-4)=(2)+log(3,2)}}} and {{{(1/2)log (4x+5)= log x}}}

Question 458375: I need help solving these problems.

and

Found 2 solutions by josmiceli, lwsshak3:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Use the rule
and the rule
and the rule
----------------------------------------

Use quadratic formula

and

check:

OK
---------

Square both sides

Complete the square:

also

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
2log3(x)-log3(x-4)=2+log3(2)
(1/2)log (4x+5)= log x
..
2log3(x)-log3(x-4)=2+log3(2)
2log3(x)-log3(x-4)-log3(2)=2
2log3(x)-(log3(x-4)+log3(2))=2
place under single log
log3[x^2/(x-4)(2)]=2
convert to exponential form (base(3) raised to log of number(2)=number[x^2/(x-4)(2)]
3^2=x^2/(x-4)(2)=9
x^2/(2x-8)=9
x^2=18x-72
x^2-18x+72=0
(x-9)(x-8)=0
x=9
or
x=8
...
(1/2)log (4x+5)= log x
(1/2)log (4x+5)- log x=0
log[(4x+5)^1/2/x]=0
10^0=(4x+5)^1/2/x=1
(4x+5)^1/2=x
square both sides
4x+5=x^2
x^2-4x-5=0
(x-5)(x+1)=0
x=5
or
x=-1 (reject, ( x>0)
RELATED QUESTIONS
I need help solving this problem: log 4 (x ^2 -3) + log 4... (answered by nerdybill)
PLEASE solve these problems PLEASE !! log(3)5+log(3)x=log(3)10 log(1/7)x=-1... (answered by Alan3354)
How do i write these as a single logarithm? 1) (log 3 - log 4) - log 2 2) log 2 +... (answered by Boreal)
I need help with the following problems: 1. 2log base 8 4- 1 over three log base 8 8... (answered by ewatrrr)
Please solve these . *WHEN I PUT LOG(3) THAT IS A SUBSCRIPT *... (answered by Alan3354)
Need help solving log base 2(5x+4) - log base... (answered by lwsshak3)
solve 2log X- log(X-2) =2 log... (answered by ikleyn)
log (6x + 5) - log 3 = log 2 - log x (answered by rapaljer,arunpaul)
log(X+3)-log X=log... (answered by Fombitz)