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LogarithmsQuestion and Answers: Page 9

Question Number 120120 Answers: 2 Comments: 0

{ ((log _a (x) = 8)),((log _b (x) = 3 )),((log _c (x) = 6)) :} ⇒ log _(abc) (x)=?

${\begin{cases} \log_{a} (x) = 8 \\ \log_{b} (x) = 3 \\ \log_{c} (x) = 6 \end{cases} \Rightarrow \log_{a b c} (x) = ?$

Question Number 119802 Answers: 2 Comments: 0

Given a,b,c real number and not equal to 1. If log _a (b)+log _b (c)+log _c (a)=0 then (log _a (b))^3 +(log _b (c))^3 +(log _c (a))^3 =?

$G i v e n a, b, c r e a l n u m b e r a n d n o t e q u a l t o 1 .$ $I f \log_{a} (b) + \log_{b} (c) + \log_{c} (a) = 0 t h e n$ ${(\log_{a} (b))}^{3} + {(\log_{b} (c))}^{3} + {(\log_{c} (a))}^{3} = ?$

Question Number 117838 Answers: 1 Comments: 0

Let be P the set of prime numbers and A=P∪{0,1} Prove that Π_(n∉A) (n/( (√(n^2 −1)))) =(2/π)(√3)

$L e t b e P t h e s e t o f p r i m e n u m b e r s a n d$ $A = P \cup {0, 1}$ $P r o v e t h a t \prod_{n \notin A} \frac{n}{\sqrt{n^{2} - 1}} = \frac{2}{π} \sqrt{3}$

Question Number 117826 Answers: 1 Comments: 0

Prove that the Euler Constant is qlso equal to lim_(x→−1) Γ(x)−(1/(x(x+1)))

$P r o v e t h a t t h e E u l e r C o n s t a n t i s q l s o e q u a l t o$ $\lim_{x \to - 1} Γ (x) - \frac{1}{x (x + 1)}$

Question Number 117816 Answers: 1 Comments: 0

find out for n≥1 Π_(k=0) ^(n−1) Γ(1+(k/n))

$f i n d o u t f o r n ⩾ 1$ $\underset{k = 0}{\prod^{n - 1}} Γ (1 + \frac{k}{n})$

Question Number 116976 Answers: 2 Comments: 0

use the formula P=Ie^(kt) ,where P is resulting population ,I is the initial population and t is measured in hours. A bacterial culture has an initial population of 10,000. If its declines to 5000 in 6 hours , what will it be at the end of 8 hours? (a) 1985 (b) 3969 (c) 2500 (d) 4353

$use the formula P = {Ie}^{kt}, where P is resulting$ $population, I is the initial population and t is$ $measured in hours . A bacterial culture$ $has an initial population of 10, 000 . If$ $its declines to 5000 in 6 hours, what$ $will it be at the end of 8 hours ?$ $(a) 1985 (b) 3969 (c) 2500 (d) 4353$

Question Number 116491 Answers: 1 Comments: 0

(0.16)^(log _(2.5) ((1/3)+(1/3^2 )+(1/3^3 )+...)) =?

${(0.16)}^{\log_{2.5} (\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + . . .)} = ?$

Question Number 116085 Answers: 0 Comments: 1

6+log_(3/2) {(1/(3(√2)))(√(4−(1/(3(√2)))(√(4−(1/(3(√2)))(√(4−(1/(3(√2)))∙∙∙))))))}= ?

$6 + \log_{\frac{3}{2}} {\frac{1}{3 \sqrt{2}} \sqrt{4 - \frac{1}{3 \sqrt{2}} \sqrt{4 - \frac{1}{3 \sqrt{2}} \sqrt{4 - \frac{1}{3 \sqrt{2}} \cdot \cdot \cdot}}}} = ?$

Question Number 115859 Answers: 2 Comments: 0

Determine, in simplest form the smallest of the three numbers x, y and z which satisfy the system { ((log _9 (x)+log _9 (y)+log _3 (z)=2)),((log _(16) (x)+log _4 (y)+log _(16) (z)=1)),((log _5 (x)+log _(25) (y)+log _(25) (z)=0)) :}

$D e t e r m i n e, i n s i m p l e s t f o r m t h e$ $s m a l l e s t o f t h e t h r e e n u m b e r s x,$ $y a n d z w h i c h s a t i s f y t h e s y s t e m$ ${\begin{cases} \log_{9} (x) + \log_{9} (y) + \log_{3} (z) = 2 \\ \log_{16} (x) + \log_{4} (y) + \log_{16} (z) = 1 \\ \log_{5} (x) + \log_{25} (y) + \log_{25} (z) = 0 \end{cases}$