precalculus question

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

please solve step by step. 

solve for x: 


Aug 30th, 2015


First, determine the domain. Any expression under log() must be positive, so x>0, x-1>0 and 4x>0 which means x>1.

Second, use log(a) + log(b) = log(a*b):
log(x) + log(x-1) = log[x(x-1)].

And log(a) = log(b) implies a = b, so

x(x-1) = 4x, or
x^2 - x = 4x. or
x^2 - 5x = 0, or
x(x-5) = 0.

x_1=0 isn't in the domain, x_2=5 is in the domain.

The answer: x=5.

Please ask if anything is unclear.
Aug 30th, 2015

Another question: 


round to three decimal points

please explain how. 


Aug 30th, 2015

Well, divide both sides by 1000 and obtain
(1.05)^(3x) = 3,

then ln (natural logarithm):
3x*ln(1.05) = ln3,  because ln(a^b) = b*ln(a),
x = ln3/(3*ln(1.05)).

Now use calculator:
x = 7.5056951018... approx= 7.506.

Aug 30th, 2015

1.If u deposit $1,000 into an account that pays 4% interest compounded continulously, how long will it take the account to grow to $2000? 

2.If u pour a cup of coffee that is 200 degress F, and set it on a desk in a room that is 68 degrees F, & 10 minutes later it is 145 degres F, what tempetrature will it be 15 min after u originally poured it?

3.A late is stocked with 1500 trout, the # of original trout alive after x yrs is given by T(x)=1,500e^-1.4x When will there be 300 of original trout left

Aug 30th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
Aug 30th, 2015
Aug 30th, 2015
Oct 17th, 2017
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer