precalculus question

Mathematics
Tutor: None Selected Time limit: 1 Day

please solve step by step. 

solve for x: 

log(x)+log(x-1)=log(4x) 

Aug 30th, 2015

Hello!

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: 

(1000)(1.05)^3x=3000 

round to three decimal points

please explain how. 

thanks 

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

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