# Recent questions tagged logarithms

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For a real number $a,$ if $\dfrac{\log_{15}a + \log_{32}a}{(\log_{15}a)(\log_{32}a)} = 4$ then $a$ must lie in the range$a>5$$3<a<4$$4<a<5$$2<a<3 1 answer 2 If \log_{2} [3+ \log_{3} \{ 4+ \log_{4} (x-1) \}] – 2 = 0 then 4x equals 1 answer 3 If 5 – \log_{10} \sqrt{1+x} + 4 \log_{10} \sqrt{1-x} = \log_{10} \frac{1}{\sqrt{1-x^{2}}}, then 100x equals 1 answer 4 If \log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B} and \log_{2} a = 1/3, then \log_{3}a equals \dfrac{2}{\text{A + B}} \;– 3 \dfrac{\text{A + B} - 3}... 1 answer 5 \dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}} equals 1 answer 6 The value of \log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right), for 1 < a \leq b cannot be equal to – 0.5$$1$$0$$ – 1$
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If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals
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If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals$\log _{2}\left ( \frac{1}{3} \right )$$-\log _{2}\left ( \frac{1}{3} \right )$$... 1 answer 9 Find the value of$x$satisfying :$\log_{10} \left (2^{x}+x-41 \right)=x \left (1-\log_{10}5 \right)$$40$$41$$-41$$0$1 answer 10 If$\log _{e}x+\log _{e}(1+x)=0,$then:$x^{2}+x-1=0$$x^{2}+x+1=0$$x^{2}+x-e=0$$x^{2}+x+e=0 2 answers 11 If \log_{x}y=100 and \log_{2}x=10, then the value of y is :2^{10}$$2^{100}$$2^{1000}$$2^{10000}$1 answer 12 If x is a real number, then$\sqrt{\log _{e}\frac{4x-x^{2}}{3}}$is a real number if and only if$1\leq x\leq 2$$-3\leq x\leq 3$$1\leq x\leq 3$$-1\leq x\leq 3 1 answer 13 The real root of the equation 2^{6x}+2^{3x+2}-21=0 is\frac{\log_{2}7}{3}$$\log_{2}9$$\frac{\log_{2}3}{3}$$\log_{2}27$1 answer 14 If$p^{3}=q^{4}=r^{5}=s^{6}$, then the value of$\log_{s}\left ( pqr \right )$is equal to$16/5$$1$$24/5$$47/10 1 answer 15 \frac{1}{\log_{2}100} – \frac{1}{\log_{4}100} + \frac{1}{\log_{5}100} – \frac{1}{\log_{10}100} + \frac{1}{\log_{20}100} – \frac{1}{\log_{25}100} + \frac{1}{\log_{5... 1 answer 16 If \log_2(5+\log_3a)=3 and \log_5(4a+12+\log_2b)=3, then a+b is equal to67$$40$$32$$59$1 answer 17 If$x$is a positive quantity such that$2^x=3^{\log_52}$, then$x$is equal to$1+\log_3\dfrac{5}{3}$$\log_58$$1+\log_5\dfrac{3}{5}$$\log_59 1 answer 18 \log_{12}81=p, then 3\bigg (\frac{4-p}{4+p}\bigg) is equal to \log_416$$\log_68$$\log_616$$\log_28$1 answer 19 If$x$is a real number such that$\log_{3}5=\log_{5}\left ( 2+x \right )$, then which of the following is true?$0<x<3$$23<x<30$$x>30$$3<x<23 1 answer 20 The value of \log_{0.008}\sqrt{5}+\log_{\sqrt{3}}81-7 is equal to1/3$$2/3$$5/6$$7/6$1 answer 21 If$\log_{10}x-\log_{10}\sqrt x=2 \log_x10$, then a possible value of$x$is given by$10$$1/100$$1/1000$None of these 1 answer 22 If$\log_{y}x=\left ( a \cdot \log_{z} y\right ) = \left ( b \cdot \log_{x}z \right )=ab,$then which of the following pairs of values for$(a,b)$is not possible?$(-2, 1...
Let $x$ and $y$ be positive real numbers such that $\log _{5}(x+y)+\log _{5}(x-y)=3$, and $\log _{2}y-\log _{2}x=1-\log_{2}3$. Then $xy$ equals$250$$25$$100$$150 1 answer 24 If \log _{x}(a-b)-\log _{x}(a+b)=\log _{x}\left(\dfrac{b}{a}\right), find \dfrac{a^{2}}{b^{2}}+\dfrac{b^{2}}{a^{2}}.4$$2$$3$$6$
If three positive real numbers $a, b$ and $c(c>a)$ are in Harmonic Progression, then $\log\left ( a+c \right )+\log\left ( a-2b+c \right )$ is equal to:$2\:\log\left ( c-... 1 answer 26 If$a=b^{2}=c^{3}=d^{4}$then the value of$\log_{a}\;(abcd)$would be$\log_{a}1+\log_{a}2+\log_{a}3+\log_{a}4$$\log_{a}24$$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$$1+\frac... 1 answer 27 What is the difference between (\log^2) (n),\log^2 n, \log (\log(n)) and (\log(n)) ^2? 1 answer 28 Choose the best alternativeIf \log_{7} \log_{5} (x+5x+x)=0; find the value of x.102None of these 1 answer 29 What is the sum of 'n' terms in the series: \log m + \log \frac{m^2}{n} + \log \frac{m^3}{n^2} + \log \frac{m^4}{n^3} + \dots + \log \frac{m^n}{n^{n-1}}?$$\log \left[\...
If $\log_{10} x - \log_{10} \sqrt{x} = 2 \log_x 10$ then a possible value of $x$ is given by$10$$\frac{1}{100}$$\frac{1}{1000}$None of these
If $\frac{1}{3} \log_3 \text{M} + 3 \log_3 \text{N} =1 + \log_{0.008} 5$, then$\text{M}^9 = \frac{9}{\text{N}}$$\text{N}^9 = \frac{9}{\text{M}}$$\text{M}^3 = \frac{3}{\te... 0 answers 32 if$\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$are in arithmetic progression, then the value of$x$is equal to$5$$4$$2$$3 0 answers 33 When the curves, y=\log_{10} x and y=x^{-1} are drawn in the x-y plane, how many times do they intersect for values x \geq 1?NeverOnceTwiceMore than twice 0 answers 34 Let u=( \log_2 x)^2 – 6 \log_2 x + 12 where x is a real number. Then the equation x^u =256, hasno solution for xexactly one solution for xexactly two distinct... 0 answers 35 If x \geq y and y 1 then the value of the expression \log_x\left(\frac{x}{y}\right) + \log_y\left(\frac{y}{x}\right) can never be-1$$-0.5$$0$$1$1 answer 36 If$\log_y x = a \cdot \log_z y = b \cdot \log_x z = ab$then which of the following pairs of values for$(a,b)$is not possible?$-2, 1/2$$1,1$$0.4, 2.5$$\pi, 1/\pi$$2,2...