SOLUTION: Given log(base x)2=.014, log(base x)3=.128, log(base x)5=.004
determine log(base x)(144x^2/25)
Algebra.Com
Question 328991: Given log(base x)2=.014, log(base x)3=.128, log(base x)5=.004
determine log(base x)(144x^2/25)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
hence
\ =\ 4\log_x(2)\ +\ 2\log_x(3)\ =\ 0.56\ +\ 0.256\ =\ 0.816)
\ =\ 2\log_x(x))
but \ =\ 1)
.
Since \ \in\ \mathbb{R})
, we are certain that 
, therefore \ =\ 1)
So we can write:
\ =\ 2\log_x(x)\ =\ 2)
And finally,
so
\ =\ 2\log_x(5)\ =\ 0.008)
The log of the product is the sum of the logs and the log of the quotient is the difference of the logs, so:
\ =\ .818\ +\ 2\ -\ 0.008\ =\ 2.808)
John
RELATED QUESTIONS
log base 5(x)+log base 25... (answered by lwsshak3)
log base 2 (x-2)+log base 2(8-x)-log base... (answered by stanbon)
log (base 3) x + log (base 5) 4x =... (answered by josgarithmetic)
find x if log 6 base 3 + log x base 3 - log 5 base... (answered by lwsshak3)
log base 2 (x-3) = log base 2... (answered by solver91311)
Log base 2 (x-2)+log base 2... (answered by Fombitz)
Log(base 2) (x+14)+log(base... (answered by MathLover1)
log(base... (answered by jsmallt9)
log base 2 (log base 3 (log base 5 of x)) = 0 (answered by stanbon)