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LogarithmsQuestion and Answers: Page 8

Question Number 143812 Answers: 1 Comments: 0

log _a (ax).log _x (ax)=log _a^2 ((1/a)) a>0 , a≠1 . So x = ?

$$\:\mathrm{log}\:_{\mathrm{a}} \left(\mathrm{ax}\right).\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{ax}\right)=\mathrm{log}\:_{\mathrm{a}^{\mathrm{2}} } \left(\frac{\mathrm{1}}{\mathrm{a}}\right) \\ $$$$\:\mathrm{a}>\mathrm{0}\:,\:\mathrm{a}\neq\mathrm{1}\:.\:\mathrm{So}\:\mathrm{x}\:=\:? \\ $$

Question Number 143811 Answers: 1 Comments: 0

{ ((5(log _y (x)+log _x (y))=26)),(( xy = 64)) :}then x^2 +y^2 +xy =?

$$\:\begin{cases}{\mathrm{5}\left(\mathrm{log}\:_{\mathrm{y}} \left(\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{x}} \left(\mathrm{y}\right)\right)=\mathrm{26}}\\{\:\mathrm{xy}\:=\:\mathrm{64}}\end{cases}\mathrm{then} \\ $$$$\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{xy}\:=? \\ $$

Question Number 143475 Answers: 1 Comments: 1

evaluate; ((((√7))^(log64) −(3)^(log_(24) 8) )/((log _2 8−log _(1/4) 64)((1/(log _4 ((1/(64))))))))

$$\:{evaluate}; \\ $$$$\frac{\left(\sqrt{\mathrm{7}}\right)^{\mathrm{log64}} −\left(\mathrm{3}\right)^{\mathrm{log}_{\mathrm{24}} \mathrm{8}} }{\left(\mathrm{log}\:_{\mathrm{2}} \mathrm{8}−\mathrm{log}\:_{\frac{\mathrm{1}}{\mathrm{4}}} \mathrm{64}\right)\left(\frac{\mathrm{1}}{\mathrm{log}\:_{\mathrm{4}} \left(\frac{\mathrm{1}}{\mathrm{64}}\right)}\right)} \\ $$

Question Number 145524 Answers: 1 Comments: 0

What is the argument of the complex numbers below (i) z = 1+e^((π/6)i) (ii) z = 1 −e^((π/6)i)

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{argument}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{numbers}\:\mathrm{below} \\ $$$$\left(\mathrm{i}\right)\:{z}\:=\:\mathrm{1}+{e}^{\frac{\pi}{\mathrm{6}}{i}} \\ $$$$\left(\mathrm{ii}\right)\:{z}\:=\:\mathrm{1}\:−{e}^{\frac{\pi}{\mathrm{6}}{i}} \\ $$

Question Number 142755 Answers: 1 Comments: 2

log_3 x^3 +log_2 x^2 =((2lg6)/(lg2))+1 find x

$$\mathrm{log}_{\mathrm{3}} \mathrm{x}^{\mathrm{3}} +\mathrm{log}_{\mathrm{2}} \mathrm{x}^{\mathrm{2}} =\frac{\mathrm{2lg6}}{\mathrm{lg2}}+\mathrm{1}\:\:\mathrm{find}\:\:\mathrm{x} \\ $$

Question Number 141365 Answers: 1 Comments: 0

log _(9/4) ((1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(...))))))))) =?

$$\:\mathrm{log}\:_{\frac{\mathrm{9}}{\mathrm{4}}} \left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{...}}}}\right)\:=? \\ $$

Question Number 140730 Answers: 1 Comments: 0

If equation 2log (x+3)=log ax has only one solution. find the value of a.

$$\mathrm{If}\:\mathrm{equation}\:\mathrm{2log}\:\left(\mathrm{x}+\mathrm{3}\right)=\mathrm{log}\:\mathrm{ax} \\ $$$$\mathrm{has}\:\mathrm{only}\:\mathrm{one}\:\mathrm{solution}.\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{a}. \\ $$

Question Number 140680 Answers: 1 Comments: 0

log _((x+2)) (7x^2 −x^3 )−log _(1/(x+2)) (x^2 −3x)≥ log _((√(x+2)) ) ((√(5−x)) )

$$\:\mathrm{log}\:_{\left(\mathrm{x}+\mathrm{2}\right)} \left(\mathrm{7x}^{\mathrm{2}} −\mathrm{x}^{\mathrm{3}} \right)−\mathrm{log}\:_{\frac{\mathrm{1}}{\mathrm{x}+\mathrm{2}}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}\right)\geqslant\:\mathrm{log}\:_{\sqrt{\mathrm{x}+\mathrm{2}}\:} \left(\sqrt{\mathrm{5}−\mathrm{x}}\:\right) \\ $$

Question Number 138091 Answers: 2 Comments: 0

If 3^((log _3 7)^x ) = 7^((log _7 3)^x ) , then the value of x will be …

$${If}\:\mathrm{3}^{\left(\mathrm{log}\:_{\mathrm{3}} \:\mathrm{7}\right)^{{x}} } \:=\:\mathrm{7}^{\left(\mathrm{log}\:_{\mathrm{7}} \:\mathrm{3}\right)^{{x}} } \:,\:{then}\:{the} \\ $$$${value}\:{of}\:{x}\:{will}\:{be}\:\ldots\: \\ $$

Question Number 137764 Answers: 1 Comments: 0

If log_2 3=a and log_3 7=b, express log_(42) 56 in terms of a and b

$$\mathrm{If}\:\mathrm{log}_{\mathrm{2}} \mathrm{3}={a}\:\mathrm{and}\:\mathrm{log}_{\mathrm{3}} \mathrm{7}={b},\:\mathrm{express} \\ $$$$\mathrm{log}_{\mathrm{42}} \mathrm{56}\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:{a}\:\mathrm{and}\:{b} \\ $$

Question Number 136256 Answers: 1 Comments: 0

log _((x−2)) (10−3x) < 2

$$\mathrm{log}\:_{\left(\mathrm{x}−\mathrm{2}\right)} \left(\mathrm{10}−\mathrm{3x}\right)\:<\:\mathrm{2} \\ $$

Question Number 136064 Answers: 1 Comments: 0

3^(log _2 (3^x −1)) = 2^(log _3 (2^x +1)) + 1

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

Question Number 134767 Answers: 0 Comments: 0

Question Number 134116 Answers: 1 Comments: 0

Question Number 133936 Answers: 2 Comments: 0

log _(x+8) (x^2 −3x−4) < 2.log _((4−x)^2 ) (∣x−4∣)

$$\mathrm{log}\:_{\mathrm{x}+\mathrm{8}} \left(\mathrm{x}^{\mathrm{2}} −\mathrm{3x}−\mathrm{4}\right)\:<\:\mathrm{2}.\mathrm{log}\:_{\left(\mathrm{4}−\mathrm{x}\right)^{\mathrm{2}} } \left(\mid\mathrm{x}−\mathrm{4}\mid\right)\: \\ $$

Question Number 133615 Answers: 2 Comments: 0

If log _4 (log _2 x)+log _2 (log _4 x)=2 then log _5 (√(x+(√x) +5)) = ?

$$\mathrm{If}\:\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{log}\:_{\mathrm{2}} \:\mathrm{x}\right)+\mathrm{log}\:_{\mathrm{2}} \left(\mathrm{log}\:_{\mathrm{4}} \:\mathrm{x}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{log}\:_{\mathrm{5}} \:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}}\:+\mathrm{5}}\:=\:? \\ $$

Question Number 131757 Answers: 0 Comments: 0

log3(√5)

$${log}\mathrm{3}\sqrt{\mathrm{5}} \\ $$

Question Number 131661 Answers: 1 Comments: 0

log _((√2) sin x) (1+cos x) = 2 −((2π)/3)≤x≤(π/3)

$$\:\:\:\mathrm{log}\:_{\sqrt{\mathrm{2}}\:\mathrm{sin}\:\mathrm{x}} \left(\mathrm{1}+\mathrm{cos}\:\mathrm{x}\right)\:=\:\mathrm{2} \\ $$$$\:−\frac{\mathrm{2}\pi}{\mathrm{3}}\leqslant\mathrm{x}\leqslant\frac{\pi}{\mathrm{3}} \\ $$

Question Number 131457 Answers: 1 Comments: 0

Find x in the equation 3^(x+1) = 4^(x−1)

$$\mathrm{Find}\:{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{3}^{{x}+\mathrm{1}} \:=\:\mathrm{4}^{{x}−\mathrm{1}} \\ $$

Question Number 131890 Answers: 1 Comments: 0

log_2 x+log_3 x=1 x=?

$${log}_{\mathrm{2}} {x}+{log}_{\mathrm{3}} {x}=\mathrm{1}\:\:\:\:\:{x}=? \\ $$

Question Number 130858 Answers: 0 Comments: 0

log [(√(mx^2 +3)) +x]=? The following subject is a node subject with a value of m

$$\mathrm{log}\:\left[\sqrt{\boldsymbol{{mx}}^{\mathrm{2}} +\mathrm{3}}\:+\boldsymbol{{x}}\right]=? \\ $$The following subject is a node subject with a value of m

Question Number 130553 Answers: 1 Comments: 0

log(x+(x^2 /2)+(x^3 /3)+(x^4 /4)+....)=?

$${log}\left({x}+\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}} }{\mathrm{3}}+\frac{{x}^{\mathrm{4}} }{\mathrm{4}}+....\right)=? \\ $$

Question Number 130244 Answers: 0 Comments: 3

Question Number 129451 Answers: 1 Comments: 0

log _(12) ((√x) + (x)^(1/4) ) = log _9 ((√x) ) x = ?

$$\:\mathrm{log}\:_{\mathrm{12}} \left(\sqrt{\mathrm{x}}\:+\:\sqrt[{\mathrm{4}}]{\mathrm{x}}\:\right)\:=\:\mathrm{log}\:_{\mathrm{9}} \left(\sqrt{\mathrm{x}}\:\right)\: \\ $$$$\:\mathrm{x}\:=\:? \\ $$

Question Number 129088 Answers: 1 Comments: 0

Question Number 128829 Answers: 0 Comments: 0

If x,y and x in HP show that log (x+z) +log (x+z−y) = 2 log (x−z)

$$\:\mathrm{If}\:\mathrm{x},\mathrm{y}\:\mathrm{and}\:\mathrm{x}\:\mathrm{in}\:\mathrm{HP}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\mathrm{log}\:\left(\mathrm{x}+\mathrm{z}\right)\:+\mathrm{log}\:\left(\mathrm{x}+\mathrm{z}−\mathrm{y}\right)\:=\:\mathrm{2}\:\mathrm{log}\:\left(\mathrm{x}−\mathrm{z}\right) \\ $$

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