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LogarithmsQuestion and Answers: Page 9

Question Number 128505 Answers: 0 Comments: 6

simplify: (5^(log_(4/5) 5) /4^(log_(4/5) 4) )

$${simplify}:\:\:\:\frac{\mathrm{5}^{{log}_{\frac{\mathrm{4}}{\mathrm{5}}} \mathrm{5}} }{\mathrm{4}^{{log}_{\frac{\mathrm{4}}{\mathrm{5}}} \mathrm{4}} } \\ $$

Question Number 126389 Answers: 2 Comments: 0

Question Number 126217 Answers: 0 Comments: 0

Question Number 124880 Answers: 2 Comments: 0

Solve for x x^(log_5 3x) =12x

$${Solve}\:{for}\:{x} \\ $$$${x}^{{log}_{\mathrm{5}} \mathrm{3}{x}} =\mathrm{12}{x} \\ $$

Question Number 121876 Answers: 0 Comments: 1

Question Number 121783 Answers: 1 Comments: 0

The number of integer values of x satisfying the inequality 2x+1<2log_2 (x+3) is ___.

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integer}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{satisfying}\: \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\mathrm{2x}+\mathrm{1}<\mathrm{2log}_{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)\:\mathrm{is}\:\_\_\_. \\ $$

Question Number 121778 Answers: 1 Comments: 2

The number of integers satisfying the inequality 3^((5/2)log_3 (12−3x)) −3^(log_2 x) >83 is ____

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{integers}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{inequality} \\ $$$$\mathrm{3}^{\left(\mathrm{5}/\mathrm{2}\right)\mathrm{log}_{\mathrm{3}} \left(\mathrm{12}−\mathrm{3x}\right)} −\mathrm{3}^{\mathrm{log}_{\mathrm{2}} \mathrm{x}} >\mathrm{83}\:\mathrm{is}\:\_\_\_\_\: \\ $$

Question Number 121387 Answers: 2 Comments: 0

(((81)^(1/log_5 9) +3^(3/log_(√6) 3) )/(409))[((√7))^(2/log_(25) 7) −(125)^(log_(25) 6) ]

$$\frac{\left(\mathrm{81}\right)^{\mathrm{1}/\mathrm{log}_{\mathrm{5}} \mathrm{9}} +\mathrm{3}^{\mathrm{3}/\mathrm{log}_{\sqrt{\mathrm{6}}} \mathrm{3}} }{\mathrm{409}}\left[\left(\sqrt{\mathrm{7}}\right)^{\mathrm{2}/\mathrm{log}_{\mathrm{25}} \mathrm{7}} −\left(\mathrm{125}\right)^{\mathrm{log}_{\mathrm{25}} \mathrm{6}} \right] \\ $$

Question Number 121278 Answers: 1 Comments: 0

The domaine of the function f(x)=((√(log_(0.5) (x^2 −7x+13))))^(−1) is;

$$\mathrm{The}\:\mathrm{domaine}\:\mathrm{of}\:\mathrm{the}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left(\sqrt{\mathrm{log}_{\mathrm{0}.\mathrm{5}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{7x}+\mathrm{13}\right)}\right)^{−\mathrm{1}} \:\mathrm{is}; \\ $$

Question Number 121201 Answers: 3 Comments: 6

Question Number 121175 Answers: 1 Comments: 0

Question Number 121138 Answers: 2 Comments: 0

Question Number 121100 Answers: 1 Comments: 0

Question Number 121045 Answers: 0 Comments: 0

Question Number 121002 Answers: 3 Comments: 0

Question Number 120927 Answers: 4 Comments: 0

Question Number 120444 Answers: 0 Comments: 0

Question Number 120380 Answers: 2 Comments: 0

Given { ((log _2 (10)=(a/(a−1)))),((log _3 (5)=(1/b))) :} find the value of 1+log _(12) (15) ?

$${Given}\:\begin{cases}{\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{10}\right)=\frac{{a}}{{a}−\mathrm{1}}}\\{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{5}\right)=\frac{\mathrm{1}}{{b}}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:\mathrm{1}+\mathrm{log}\:_{\mathrm{12}} \left(\mathrm{15}\right)\:? \\ $$

Question Number 120120 Answers: 2 Comments: 0

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

$$\begin{cases}{\mathrm{log}\:_{{a}} \left({x}\right)\:=\:\mathrm{8}}\\{\mathrm{log}\:_{{b}} \left({x}\right)\:=\:\mathrm{3}\:}\\{\mathrm{log}\:_{{c}} \left({x}\right)\:=\:\mathrm{6}}\end{cases}\:\Rightarrow\:\mathrm{log}\:_{{abc}} \:\left({x}\right)=? \\ $$

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 =?

$${Given}\:{a},{b},{c}\:{real}\:{number}\:{and}\:{not}\:{equal}\:{to}\:\mathrm{1}. \\ $$$${If}\:\mathrm{log}\:_{{a}} \left({b}\right)+\mathrm{log}\:_{{b}} \left({c}\right)+\mathrm{log}\:_{{c}} \left({a}\right)=\mathrm{0}\:{then}\: \\ $$$$\left(\mathrm{log}\:_{{a}} \left({b}\right)\right)^{\mathrm{3}} +\left(\mathrm{log}\:_{{b}} \left({c}\right)\right)^{\mathrm{3}} +\left(\mathrm{log}\:_{{c}} \left({a}\right)\right)^{\mathrm{3}} =? \\ $$

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)

$$\:\:{Let}\:{be}\:{P}\:\:{the}\:{set}\:{of}\:{prime}\:{numbers}\:{and}\: \\ $$$${A}={P}\cup\left\{\mathrm{0},\mathrm{1}\right\} \\ $$$${Prove}\:{that}\:\:\:\underset{{n}\notin{A}} {\prod}\:\frac{{n}}{\:\sqrt{{n}^{\mathrm{2}} −\mathrm{1}}}\:=\frac{\mathrm{2}}{\pi}\sqrt{\mathrm{3}}\: \\ $$

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)))

$$\:\:{Prove}\:{that}\:{the}\:{Euler}\:{Constant}\:{is}\:{qlso}\:{equal}\:{to} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}} {\mathrm{lim}}\:\:\Gamma\left({x}\right)−\frac{\mathrm{1}}{{x}\left({x}+\mathrm{1}\right)} \\ $$

Question Number 117816 Answers: 1 Comments: 0

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

$$\:\:{find}\:{out}\:\:\:{for}\:{n}\geqslant\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{k}=\mathrm{0}} {\overset{{n}−\mathrm{1}} {\prod}}\Gamma\left(\mathrm{1}+\frac{{k}}{{n}}\right) \\ $$$$ \\ $$

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

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

Question Number 116491 Answers: 1 Comments: 0

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

$$\left(\mathrm{0}.\mathrm{16}\right)^{\mathrm{log}\:_{\mathrm{2}.\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+...\right)} \:=? \\ $$

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)))∙∙∙))))))}= ?

$$\mathrm{6}+\mathrm{log}_{\frac{\mathrm{3}}{\mathrm{2}}} \left\{\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\sqrt{\mathrm{4}−\frac{\mathrm{1}}{\mathrm{3}\sqrt{\mathrm{2}}}\centerdot\centerdot\centerdot}}}\right\}=\:? \\ $$

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