Question and Answers Forum

LogarithmsQuestion and Answers: Page 10

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)) :}

Question Number 115341 Answers: 1 Comments: 0

If log tan 1°+log tan 2°+log tan 3°+...+log tan 89°=p then p^2 +3 =

$${If}\:\mathrm{log}\:\mathrm{tan}\:\mathrm{1}°+\mathrm{log}\:\mathrm{tan}\:\mathrm{2}°+\mathrm{log}\:\mathrm{tan}\:\mathrm{3}°+...+\mathrm{log}\:\mathrm{tan}\:\mathrm{89}°={p} \\ $$$${then}\:{p}^{\mathrm{2}} +\mathrm{3}\:=\: \\ $$

Question Number 115268 Answers: 1 Comments: 0

(√(4^x −5.2^(x+1) +25)) +(√(9^x −2.3^(x+2) +17)) ≤ 2^x −5

$$\sqrt{\mathrm{4}^{{x}} −\mathrm{5}.\mathrm{2}^{{x}+\mathrm{1}} +\mathrm{25}}\:+\sqrt{\mathrm{9}^{{x}} −\mathrm{2}.\mathrm{3}^{{x}+\mathrm{2}} +\mathrm{17}}\:\leqslant\:\mathrm{2}^{{x}} −\mathrm{5} \\ $$

Question Number 115246 Answers: 0 Comments: 1

5^((x+1)^2 ) + 625 ≤ 5^(x^2 +2) + 5^(2x+3)

$$\:\:\:\:\mathrm{5}^{\left({x}+\mathrm{1}\right)^{\mathrm{2}} } \:+\:\mathrm{625}\:\leqslant\:\mathrm{5}^{{x}^{\mathrm{2}} +\mathrm{2}} \:+\:\mathrm{5}^{\mathrm{2}{x}+\mathrm{3}} \\ $$

Question Number 115238 Answers: 2 Comments: 0

64^(x^2 −(3/4)x) ≤ ((√8))^x^3

$$\:\:\:\mathrm{64}^{{x}^{\mathrm{2}} −\frac{\mathrm{3}}{\mathrm{4}}{x}} \:\leqslant\:\left(\sqrt{\mathrm{8}}\right)^{{x}^{\mathrm{3}} } \: \\ $$

Question Number 113862 Answers: 1 Comments: 0

Question Number 113872 Answers: 0 Comments: 0

log_(1/( (√2))) sinx >0, x∈[0,4π], then the number of values of x which are integral multiples of (π/4), is.

$$\mathrm{log}_{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} \mathrm{sinx}\:>\mathrm{0},\:\mathrm{x}\in\left[\mathrm{0},\mathrm{4}\pi\right],\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{number}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{which}\:\mathrm{are} \\ $$$$\mathrm{integral}\:\mathrm{multiples}\:\mathrm{of}\:\frac{\pi}{\mathrm{4}},\:\mathrm{is}. \\ $$

Question Number 113811 Answers: 1 Comments: 0

If log_(12) 27=a, express log_6 16 in terms of a.

$$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{27}=\mathrm{a},\:\mathrm{express}\:\mathrm{log}_{\mathrm{6}} \mathrm{16}\:\mathrm{in}\:\mathrm{terms} \\ $$$$\mathrm{of}\:\mathrm{a}. \\ $$

Question Number 113803 Answers: 3 Comments: 0

If a=log_(24) 12, b=log_(36) 24 and c=log_(48) 36, then 1+abc is equal to (A) 2ab (B) 2ac (C) 2bc (D) 0

$$\mathrm{If}\:\mathrm{a}=\mathrm{log}_{\mathrm{24}} \mathrm{12},\:\mathrm{b}=\mathrm{log}_{\mathrm{36}} \mathrm{24}\:\mathrm{and} \\ $$$$\mathrm{c}=\mathrm{log}_{\mathrm{48}} \mathrm{36},\:\mathrm{then}\:\mathrm{1}+\mathrm{abc}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:\mathrm{2ab}\:\left(\mathrm{B}\right)\:\mathrm{2ac}\:\left(\mathrm{C}\right)\:\mathrm{2bc}\:\left(\mathrm{D}\right)\:\mathrm{0} \\ $$

Question Number 113800 Answers: 1 Comments: 0

log (ab)−log∣b∣ = A. log(a) B. log ∣a∣ C. −log(a) D. None of these.

$$\mathrm{log}\:\left(\mathrm{ab}\right)−\mathrm{log}\mid\mathrm{b}\mid\:= \\ $$$$ \\ $$$$\mathrm{A}.\:\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{B}.\:\mathrm{log}\:\mid\mathrm{a}\mid\:\mathrm{C}.\:−\mathrm{log}\left(\mathrm{a}\right)\:\mathrm{D}. \\ $$$$\mathrm{None}\:\mathrm{of}\:\mathrm{these}. \\ $$

Question Number 113426 Answers: 1 Comments: 0

Question Number 112808 Answers: 1 Comments: 0

Question Number 112773 Answers: 1 Comments: 0

∫(( (√x))/(x^3 +1))dx Please help

$$\int\frac{\:\sqrt{{x}}}{{x}^{\mathrm{3}} +\mathrm{1}}{dx} \\ $$$${Please}\:{help} \\ $$

Question Number 111721 Answers: 1 Comments: 0

If b>1,x>0 and (2x)^(log_b 2) −(3x)^(log_b 3) =0, then x is

$$\mathrm{If}\:\mathrm{b}>\mathrm{1},\mathrm{x}>\mathrm{0}\:\mathrm{and}\:\left(\mathrm{2x}\right)^{\mathrm{log}_{\mathrm{b}} \mathrm{2}} −\left(\mathrm{3x}\right)^{\mathrm{log}_{\mathrm{b}} \mathrm{3}} =\mathrm{0}, \\ $$$$\mathrm{then}\:\mathrm{x}\:\mathrm{is} \\ $$

Question Number 110280 Answers: 0 Comments: 0

Question Number 110183 Answers: 3 Comments: 0

(√★)((be)/(math))(√★) log _2 (x)+log _3 (x)+log _4 (x)=1 x=?

$$\:\:\:\sqrt{\bigstar}\frac{{be}}{{math}}\sqrt{\bigstar} \\ $$$$\:\:\mathrm{log}\:_{\mathrm{2}} \left({x}\right)+\mathrm{log}\:_{\mathrm{3}} \left({x}\right)+\mathrm{log}\:_{\mathrm{4}} \left({x}\right)=\mathrm{1} \\ $$$$\:\:\:{x}=? \\ $$

Question Number 109963 Answers: 1 Comments: 0

Question Number 107304 Answers: 2 Comments: 0

⋎bemath⋎ (1)Find domain of function f(x)= (√(log _(0.2) (((x+2)/(x−1)))−1)) (2) ((sin^2 (((9π)/8)−2x)−sin^2 (((7π)/8)−2x))/(sin (2018π+4x)))=?

$$\:\:\:\curlyvee{bemath}\curlyvee \\ $$$$\left(\mathrm{1}\right){Find}\:{domain}\:{of}\:{function}\: \\ $$$${f}\left({x}\right)=\:\sqrt{\mathrm{log}\:_{\mathrm{0}.\mathrm{2}} \left(\frac{{x}+\mathrm{2}}{{x}−\mathrm{1}}\right)−\mathrm{1}}\: \\ $$$$\left(\mathrm{2}\right)\:\frac{\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{9}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)−\mathrm{sin}\:^{\mathrm{2}} \left(\frac{\mathrm{7}\pi}{\mathrm{8}}−\mathrm{2}{x}\right)}{\mathrm{sin}\:\left(\mathrm{2018}\pi+\mathrm{4}{x}\right)}=? \\ $$

Question Number 107318 Answers: 1 Comments: 0

⊚bemath⊚ 6^(log _((x−1)) (((20−12x)/(x−7)))) −36 >0

$$\:\:\:\:\:\circledcirc{bemath}\circledcirc \\ $$$$\mathrm{6}^{\mathrm{log}\:_{\left({x}−\mathrm{1}\right)} \left(\frac{\mathrm{20}−\mathrm{12}{x}}{{x}−\mathrm{7}}\right)} −\mathrm{36}\:>\mathrm{0} \\ $$

Question Number 107153 Answers: 1 Comments: 0

@bemath@ (((14)/5))^(((28)/(√x))−5) = ((5/(14)))^((5/(√x))−160)

$$\:\:\:\:\:\:@{bemath}@ \\ $$$$\left(\frac{\mathrm{14}}{\mathrm{5}}\right)^{\frac{\mathrm{28}}{\sqrt{{x}}}−\mathrm{5}} =\:\left(\frac{\mathrm{5}}{\mathrm{14}}\right)^{\frac{\mathrm{5}}{\sqrt{{x}}}−\mathrm{160}} \\ $$

Question Number 106996 Answers: 1 Comments: 1

@bemath@ log _(∣2x−(1/2)∣) (x+1+(1/x))≥log _(∣2x−(1/2)∣) (x^2 +1+(1/x^2 ))

$$\:\:\:\:\:\:\:@{bemath}@ \\ $$$$\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}+\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\geqslant\mathrm{log}\:_{\mid\mathrm{2}{x}−\frac{\mathrm{1}}{\mathrm{2}}\mid} \left({x}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right) \\ $$

Question Number 106888 Answers: 2 Comments: 0

@bemath@ given { ((f(x)=log _2 (sin x)+log _2 (cos x))),((g(x)=log _2 (cos 2x)+log _2 (cos 4x))) :} find f((π/(48)))+g((π/(48))) .

$$@\mathrm{bemath}@ \\ $$$$\mathfrak{g}\mathrm{iven}\:\begin{cases}{\mathrm{f}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{sin}\:\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{x}\right)}\\{\mathrm{g}\left(\mathrm{x}\right)=\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{2x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{cos}\:\mathrm{4x}\right)}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{f}\left(\frac{\pi}{\mathrm{48}}\right)+\mathrm{g}\left(\frac{\pi}{\mathrm{48}}\right)\:. \\ $$

Question Number 106688 Answers: 0 Comments: 0

Σ_(k=0) ^∞ (((−1)^n )/((2n+1)!))z^(2n−14) =?

$$\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)!}{z}^{\mathrm{2}{n}−\mathrm{14}} =? \\ $$

Question Number 106024 Answers: 2 Comments: 1

log _4 (5x−6).log _x (256)=8

$$\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{5x}−\mathrm{6}\right).\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{256}\right)=\mathrm{8} \\ $$

Question Number 105380 Answers: 1 Comments: 1

Question Number 105235 Answers: 1 Comments: 0

(x−2)^(log _2 (x^2 −5x+5)) > (x−2)^(log _2 (x−3))

$$\left({x}−\mathrm{2}\right)^{\mathrm{log}\:_{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{5}\right)} \:>\:\left({x}−\mathrm{2}\right)^{\mathrm{log}\:_{\mathrm{2}} \left({x}−\mathrm{3}\right)} \\ $$

Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10 Pg 11 Pg 12 Pg 13 Pg 14

Contact: [email protected]