Question and Answers Forum

LogarithmsQuestion and Answers: Page 3

Question Number 196249 Answers: 0 Comments: 0

log_a x=30 log_b x=70 log_(ab) x=?

$${log}_{{a}} {x}=\mathrm{30} \\ $$$${log}_{{b}} {x}=\mathrm{70} \\ $$$${log}_{{ab}} {x}=? \\ $$

Question Number 196026 Answers: 1 Comments: 0

∫^( +∞) _( 0) (((lnt)^2 )/(1+t^2 ))dt

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\left({lnt}\right)^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 195895 Answers: 1 Comments: 0

Calcul ∫^( (π/2)) _( 0) t(√(tan(t))) dt

$$\mathrm{Calcul}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{t}\sqrt{\mathrm{tan}\left(\mathrm{t}\right)}\:\mathrm{dt} \\ $$

Question Number 195753 Answers: 1 Comments: 0

Calculer ∫^( 1) _( 0) ((ln^2 t)/( (√(1−t^2 ))))dt

$$\mathrm{Calculer}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} {t}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{dt} \\ $$

Question Number 195087 Answers: 2 Comments: 0

Question Number 194961 Answers: 1 Comments: 0

Question Number 194736 Answers: 0 Comments: 2

( log _(sin x cos x) (cos x))( log _(sin x cos x) (sin x))=(1/4)

$$\:\:\:\: \\ $$$$ \left(\:\mathrm{log}\:_{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}} \:\left(\mathrm{cos}\:\mathrm{x}\right)\right)\left(\:\mathrm{log}\:_{\mathrm{sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}} \left(\mathrm{sin}\:\mathrm{x}\right)\right)=\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\:\: \\ $$

Question Number 194613 Answers: 2 Comments: 0

log _(4x) (x)+ log _(x/2) (x)= 2

$$\:\:\:\:\: \\ $$$$\:\:\mathrm{log}\:_{\mathrm{4x}} \left(\mathrm{x}\right)+\:\mathrm{log}\:_{\mathrm{x}/\mathrm{2}} \left(\mathrm{x}\right)=\:\mathrm{2}\: \\ $$

Question Number 194165 Answers: 1 Comments: 0

Question Number 193656 Answers: 0 Comments: 1

please can someone solves this

$${please}\:{can}\:{someone}\:{solves}\:{this}\: \\ $$

Question Number 193360 Answers: 2 Comments: 0

If x = 2^p and y = 4^q then prove that log_2 (x^3 y) = 3p + 2q

$$\mathrm{If}\:{x}\:=\:\mathrm{2}^{{p}} \:\mathrm{and}\:{y}\:=\:\mathrm{4}^{{q}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{log}_{\mathrm{2}} \left({x}^{\mathrm{3}} {y}\right)\:=\:\mathrm{3}{p}\:+\:\mathrm{2}{q} \\ $$

Question Number 193295 Answers: 2 Comments: 0

Find the value of x from the following equations: 4^((x/y) + (y/x)) = 32 log_3 (x − y) + log_3 (x + y) = 1

$$\boldsymbol{\mathrm{Find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{{x}}\:\boldsymbol{\mathrm{from}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{following}} \\ $$$$\boldsymbol{\mathrm{equations}}: \\ $$$$\mathrm{4}^{\frac{{x}}{{y}}\:+\:\frac{{y}}{{x}}} \:=\:\mathrm{32} \\ $$$$\mathrm{log}_{\mathrm{3}} \left({x}\:−\:{y}\right)\:+\:\mathrm{log}_{\mathrm{3}} \left({x}\:+\:{y}\right)\:=\:\mathrm{1} \\ $$

Question Number 193253 Answers: 1 Comments: 0

Select the correct option with explaination: If (1/3)log_3 M + 3log_3 N = 1 + log_(0.008) 5 then a. M^9 = (9/N) b. N^9 = (9/M) c. M^3 = (3/N) d. N^3 = (3/M)

$$\boldsymbol{\mathrm{Select}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}\:\boldsymbol{\mathrm{with}}\: \\ $$$$\boldsymbol{\mathrm{explaination}}: \\ $$$$\mathrm{If}\:\frac{\mathrm{1}}{\mathrm{3}}\mathrm{log}_{\mathrm{3}} {M}\:+\:\mathrm{3log}_{\mathrm{3}} {N}\:=\:\mathrm{1}\:+\:\mathrm{log}_{\mathrm{0}.\mathrm{008}} \mathrm{5}\:\mathrm{then} \\ $$$$\mathrm{a}.\:{M}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{N}} \\ $$$$\mathrm{b}.\:{N}^{\mathrm{9}} \:=\:\frac{\mathrm{9}}{{M}} \\ $$$$\mathrm{c}.\:{M}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{N}} \\ $$$$\mathrm{d}.\:{N}^{\mathrm{3}} \:=\:\frac{\mathrm{3}}{{M}}\: \\ $$

Question Number 193230 Answers: 1 Comments: 0

Choose the correct option: If a, b and c are consecutive positive integers and log(1 + ac) = 2k then the value of k is: a) log a b) log b c) 2 d) 1 Give the explaination also.

$$\boldsymbol{\mathrm{Choose}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{correct}}\:\boldsymbol{\mathrm{option}}: \\ $$$$\mathrm{If}\:{a},\:{b}\:\mathrm{and}\:{c}\:\mathrm{are}\:\mathrm{consecutive}\:\mathrm{positive} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{log}\left(\mathrm{1}\:+\:{ac}\right)\:=\:\mathrm{2}{k}\:\mathrm{then}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{is}: \\ $$$$\left.\mathrm{a}\right)\:\mathrm{log}\:{a} \\ $$$$\left.\mathrm{b}\right)\:\mathrm{log}\:{b} \\ $$$$\left.\mathrm{c}\right)\:\mathrm{2} \\ $$$$\left.\mathrm{d}\right)\:\mathrm{1} \\ $$$$\boldsymbol{\mathrm{Give}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{explaination}}\:\boldsymbol{\mathrm{also}}. \\ $$

Question Number 193183 Answers: 1 Comments: 0

There exists a unique positive integer a for which The sum u = Σ_(n=1) ^(2023) ⌊((n^2 −na)/5)⌋ is an integer strictly between −1000 & 1000 find a+u.

$$ \\ $$$${There}\:{exists}\:{a}\:{unique}\:{positive}\:{integer}\:{a}\:{for} \\ $$$${which}\:{The}\:{sum}\:{u}\:\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{2023}} {\sum}}\lfloor\frac{{n}^{\mathrm{2}} −{na}}{\mathrm{5}}\rfloor\:{is}\:{an}\:{integer} \\ $$$${strictly}\:{between}\:−\mathrm{1000}\:\&\:\mathrm{1000}\:{find}\:{a}+{u}. \\ $$

Question Number 192918 Answers: 1 Comments: 0