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LogarithmsQuestion and Answers: Page 1

Question Number 227232 Answers: 0 Comments: 0

(64−(8π+4π))−(8π−(4(tan^(−1) 2+4tan^(−1) (1/2)−2)+8(π−2)))−(64−(16π+8π−16(tan^(−1) 2+4tan^(−1) (1/2)−2)))−(3.2+2+(32tan^(−1) ((4.8)/(6.4))−32sin tan^(−1) ((4.8)/(6.4)))−π)+4(tan^(−1) 2+4tan^(−1) (1/2)−2)

$$\left(\mathrm{64}−\left(\mathrm{8}\pi+\mathrm{4}\pi\right)\right)−\left(\mathrm{8}\pi−\left(\mathrm{4}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right)+\mathrm{8}\left(\pi−\mathrm{2}\right)\right)\right)−\left(\mathrm{64}−\left(\mathrm{16}\pi+\mathrm{8}\pi−\mathrm{16}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right)\right)\right)−\left(\mathrm{3}.\mathrm{2}+\mathrm{2}+\left(\mathrm{32tan}^{−\mathrm{1}} \frac{\mathrm{4}.\mathrm{8}}{\mathrm{6}.\mathrm{4}}−\mathrm{32sin}\:\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{4}.\mathrm{8}}{\mathrm{6}.\mathrm{4}}\right)−\pi\right)+\mathrm{4}\left(\mathrm{tan}^{−\mathrm{1}} \mathrm{2}+\mathrm{4tan}^{−\mathrm{1}} \frac{\mathrm{1}}{\mathrm{2}}−\mathrm{2}\right) \\ $$

Question Number 227192 Answers: 2 Comments: 0

x^(log 2x) = 5 ⇒x= ?

$$\:\:\:\:{x}^{\mathrm{log}\:\mathrm{2}{x}} \:=\:\mathrm{5}\:\Rightarrow{x}=\:? \\ $$

Question Number 223514 Answers: 1 Comments: 0

log _8 [log _2 {log _3 (4^x +17)}]=(1/3) x=??

$$\mathrm{log}\:_{\mathrm{8}} \left[\mathrm{log}\:_{\mathrm{2}} \left\{\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{4}^{{x}} +\mathrm{17}\right)\right\}\right]=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$${x}=?? \\ $$

Question Number 223513 Answers: 2 Comments: 0

If x=log _a bc , y=log _b ca , z=log _c ab prove that x+y+z=xyz−2

$${If}\:{x}=\mathrm{log}\:_{{a}} {bc}\:,\:{y}=\mathrm{log}\:_{{b}} {ca}\:,\:{z}=\mathrm{log}\:_{{c}} {ab} \\ $$$${prove}\:{that}\:{x}+{y}+{z}={xyz}−\mathrm{2} \\ $$

Question Number 223512 Answers: 1 Comments: 0

If ((log x)/(y−z))=((log y)/(z−x))=((log z)/(x−y)) prove xyz=1

$${If}\:\frac{\mathrm{log}\:{x}}{{y}−{z}}=\frac{\mathrm{log}\:{y}}{{z}−{x}}=\frac{\mathrm{log}\:{z}}{{x}−{y}} \\ $$$${prove}\:{xyz}=\mathrm{1} \\ $$

Question Number 222929 Answers: 0 Comments: 0

Question Number 222799 Answers: 0 Comments: 1

x^x^y =9^(xy) x+y=1

$${x}^{{x}^{{y}} } =\mathrm{9}^{{xy}} \\ $$$${x}+{y}=\mathrm{1} \\ $$

Question Number 222697 Answers: 1 Comments: 0

Question Number 222679 Answers: 2 Comments: 0

If x=Π_(x=1) ^(10) x then (1/(log _2 x))+(1/(log _3 x))+(1/(log _4 x))...+(1/(log _(10) x))=??

$${If}\:{x}=\underset{{x}=\mathrm{1}} {\overset{\mathrm{10}} {\prod}}{x}\:{then}\:\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{2}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{3}} {x}}+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} {x}}...+\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{10}} {x}}=?? \\ $$

Question Number 222104 Answers: 2 Comments: 0

log _4 x − log _x^2 8 = 1 x =?

$$\:\:\:\:\mathrm{log}\:_{\mathrm{4}} \:\mathrm{x}\:−\:\mathrm{log}\:_{\mathrm{x}^{\mathrm{2}} } \:\mathrm{8}\:=\:\mathrm{1} \\ $$$$\:\:\:\:\mathrm{x}\:=?\: \\ $$

Question Number 222007 Answers: 0 Comments: 5

x(√(1+x^2 ))+log(x+(√(1+x^2 )))=12.5 find x^2 (answer should not be in decimal)

$$\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\sqrt{\mathrm{1}+\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\right)=\mathrm{12}.\mathrm{5} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{x}}^{\mathrm{2}} \:\left(\mathrm{answer}\:\mathrm{should}\:\mathrm{not}\:\mathrm{be}\:\mathrm{in}\:\mathrm{decimal}\right) \\ $$

Question Number 221896 Answers: 1 Comments: 0

If log _(10) 7=a ,then log _(10) ((1/(70)))=?

$${If}\:\mathrm{log}\underset{\mathrm{10}} {\:}\mathrm{7}={a}\:,{then}\:\mathrm{log}\underset{\mathrm{10}} {\:}\left(\frac{\mathrm{1}}{\mathrm{70}}\right)=? \\ $$

Question Number 221869 Answers: 1 Comments: 0

if a^(3−x) .b^(5x) =a^(5+x) .b^(3x) then show that xlog ((b/a))=log a

$${if}\:{a}^{\mathrm{3}−{x}} .{b}^{\mathrm{5}{x}} ={a}^{\mathrm{5}+{x}} .{b}^{\mathrm{3}{x}} \:{then}\:{show}\:{that} \\ $$$${x}\mathrm{log}\:\left(\frac{{b}}{{a}}\right)=\mathrm{log}\:{a} \\ $$

Question Number 221853 Answers: 2 Comments: 3

find x where log _8 x−log _4 x−log _2 x=11

$${find}\:{x}\:{where} \\ $$$$\mathrm{log}\underset{\mathrm{8}} {\:}{x}−\mathrm{log}\underset{\mathrm{4}} {\:}{x}−\mathrm{log}\underset{\mathrm{2}} {\:}{x}=\mathrm{11} \\ $$

Question Number 221760 Answers: 1 Comments: 0

Question Number 221397 Answers: 0 Comments: 1

Question Number 221103 Answers: 0 Comments: 0

Prove : ∀x∈IR, ∀n∈IN^∗ ∫^( (π/2)) _( 0) ch(2xt)cos^(2n) (t) dt ≤ e^(x^2 /n) ∫^( (π/2)) _( 0) cos^(2n) (t) dt

$$\mathrm{Prove}\::\:\:\:\:\:\forall\mathrm{x}\in\mathrm{IR},\:\forall\mathrm{n}\in\mathrm{IN}^{\ast} \: \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{ch}\left(\mathrm{2xt}\right)\mathrm{cos}^{\mathrm{2n}} \left(\mathrm{t}\right)\:\mathrm{dt}\:\leqslant\:\mathrm{e}^{\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}} \underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{cos}^{\mathrm{2n}} \left(\mathrm{t}\right)\:\mathrm{dt} \\ $$

Question Number 218279 Answers: 2 Comments: 0

Evaluate: (4^(log_(5/4) 4) /5^(log_(5/4) 5) ) Show workings please.

$$\mathrm{Evaluate}: \\ $$$$\:\:\:\:\:\frac{\mathrm{4}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{4}} }{\mathrm{5}^{\mathrm{log}_{\frac{\mathrm{5}}{\mathrm{4}}} \mathrm{5}} } \\ $$$$\mathrm{Show}\:\mathrm{workings}\:\mathrm{please}. \\ $$

Question Number 217691 Answers: 3 Comments: 0

Question Number 215951 Answers: 1 Comments: 0

E_n = 3^E_(n−1) , n≥2 find the unit digit of E_(1000)

$${E}_{{n}} \:=\:\mathrm{3}^{{E}_{{n}−\mathrm{1}} } ,\:{n}\geqslant\mathrm{2} \\ $$$${find}\:{the}\:{unit}\:{digit}\:{of}\:{E}_{\mathrm{1000}} \\ $$

Question Number 215840 Answers: 2 Comments: 2

log _(24) 3= a and log _(24) 6 = (b/6) log _(√8) (b−4a)= ?

$$\:\:\:\mathrm{log}\:_{\mathrm{24}} \:\mathrm{3}=\:{a}\:\mathrm{and}\:\mathrm{log}\:_{\mathrm{24}} \:\mathrm{6}\:=\:\frac{{b}}{\mathrm{6}} \\ $$$$\:\:\:\mathrm{log}\:_{\sqrt{\mathrm{8}}} \:\left({b}−\mathrm{4}{a}\right)=\:? \\ $$

Question Number 215089 Answers: 1 Comments: 0

log _2 x + log _3 (x+1) = 5 x = ?

$$\:\:\mathrm{log}\:_{\mathrm{2}} \:\mathrm{x}\:+\:\mathrm{log}\:_{\mathrm{3}} \:\left(\mathrm{x}+\mathrm{1}\right)\:=\:\mathrm{5}\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 213923 Answers: 3 Comments: 0

Question Number 212645 Answers: 0 Comments: 0

{ ((x=2+ log _2 log _2 y)),((y=2 log _2 z )),((z=2+ log _2 log _2 x )) :}

$$\:\:\begin{cases}{\mathrm{x}=\mathrm{2}+\:\mathrm{log}\:_{\mathrm{2}} \mathrm{log}\:_{\mathrm{2}} \mathrm{y}}\\{\mathrm{y}=\mathrm{2}\:\mathrm{log}\:_{\mathrm{2}} \mathrm{z}\:}\\{\mathrm{z}=\mathrm{2}+\:\mathrm{log}\:_{\mathrm{2}} \:\mathrm{log}\:_{\mathrm{2}} \mathrm{x}\:}\end{cases} \\ $$

Question Number 212515 Answers: 1 Comments: 1

The numbers of pairs of natural numbers (x,y) with x,y ≤ 33 that satisfy 5 ∣ 3^x^(y−1) + 2^y^(2x) is ... (A) 295 (B) 296 (C) 297 (D) 298 (E) 299

$$\:\:\mathrm{The}\:\mathrm{numbers}\:\mathrm{of}\:\mathrm{pairs}\:\mathrm{of}\:\mathrm{natural}\: \\ $$$$\:\:\:\mathrm{numbers}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{with}\:\mathrm{x},\mathrm{y}\:\leqslant\:\mathrm{33}\:\mathrm{that}\: \\ $$$$\:\:\:\mathrm{satisfy}\:\mathrm{5}\:\mid\:\mathrm{3}^{\mathrm{x}^{\mathrm{y}−\mathrm{1}} } \:+\:\mathrm{2}^{\mathrm{y}^{\mathrm{2x}} } \:\mathrm{is}\:...\: \\ $$$$\:\:\left(\mathrm{A}\right)\:\mathrm{295}\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{296}\:\:\:\:\:\:\:\left(\mathrm{C}\right)\:\mathrm{297}\:\:\:\:\:\:\left(\mathrm{D}\right)\:\mathrm{298}\:\:\:\left(\mathrm{E}\right)\:\mathrm{299} \\ $$

Question Number 212101 Answers: 0 Comments: 0

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