SOLUTION: my problem is: log (base 4) 9x^2 = log (base 2)(5x-8) i think i have to switch the base on the left hand side to 2 which would give me log (base 2) 9x^2 ----------- -----

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: my problem is: log (base 4) 9x^2 = log (base 2)(5x-8) i think i have to switch the base on the left hand side to 2 which would give me log (base 2) 9x^2 ----------- -----       Log On


   

Question 96003: my problem is:
log (base 4) 9x^2 = log (base 2)(5x-8)
i think i have to switch the base on the left hand side to 2 which would give me

log (base 2) 9x^2
----------------- = log (base 2)(5x-8)
log (base 2) 4
i dont even know if thats right..but after that im completely lost though...any help would be appreciated, thanks.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you are right about changing the base ... 2^2=4 so log(base2)4=2 ... so log(base2)9x^2=2(log(base2)(5x-8))

multiplying a log by 2 means squaring the argument ... 9x^2=(5x-8)^2 ... taking square root gives 3x=5x-8 and -3x=5x-8

so x=4 and x=1 ... but remember, logs are undefined for negative arguments [5(1)-8=-3] ... so 4 is the solution