Hello,
You should know some formulae for logarithms. Then, 1) and 2) are easy.
For 3), you see that x-1>0 (in order for the log to be defined.)
Then, the equation becomes .
Bye.
could somebody help me with these questions...being able to see the work would be awesome and incredibly helpful! thank you!
1) write as a single logarithm and solve :
2log3(12)-2log3(4)
2)write as a single logarithm:
log3(x+2)-logx(2x-1)+log3(5)
3)solve for x: logx(x-1)=log8(x-1)
HEY,
3) Since the question is asking u to solve to find x
then x has a value
just looking at the eqation you can conclude that
(x=8), since its similar and there is an = sign
soooo the bases have to be the same too.
For 1 and 2, dude its veryyyyy simple
you just need to know 4 basic rules.
1) nLog x = Log x^n
2) Log(base-C)A + Log(base-C)B = Log(baseC)A*B
3) Log(base-C)A - Log(base-C)B = Log(baseC)A/B
4) Log (base-x)x^n = n Log (base-x)x =n
* = times
Back to ur questions
1) 2log3(12) - 2log3(4)
if i am correct 3 is the base????
Log (base3) 12^2 - Log (base3) 4^2
Log (base3) 144 - Log (base3) 16
Log (base3) 144/16
Log (base3) 9 (thats the single logarithm)
We can further simplify it to solve it
Log (base3) 3^2
2 Log (base3) 3
= 2
2) Log 3(x+2) - Log x(2x-1) + log 3(5)
= Log (3x+6) - log (2x^2 -x) + log 15
= log (3x+6)/(2x^2 -x) * 15
= log (45x+90)/(2x^2 -x)
I hope this helpes
cheers