Algebra-Functions

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Exponential

solution \frac{1}{1\cdot2}-\frac{1}{2\cdot3}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+........\,

solution Show that \frac{1\cdot2}{1!}+\frac{2\cdot3}{2!}+\frac{3\cdot4}{3!}+...........=3e\,

solution Find the sum of the infinite series \frac{1}{2}-\frac{1}{2\cdot2^2}+\frac{1}{3\cdot2^3}-.........\,

solution Find the sum of the infinite series \frac{1}{1\cdot3}+\frac{1}{2}[\frac{1}{3\cdot5}]+\frac{1}{3}[\frac{1}{5\cdot7}].........\,

Logarithmic

solution If a not equal to 1,m,n are positive real numbers, then show that \log_a(\frac{m}{n})=\log_a(m)-\log_a(n)\,

solution If a not equal to 1 and m,n are positive real numbers, then \log_a(mn)=\log_a(m)+\log_a(n)\,

solution If a not equal to 1 and m,k are positive real numbers, then \log_a(m^k)=k\cdot\log_a(m)\,

solution Rule of change of base,if a and b not equal to 1 and m is a positive real number, then \log_a(m)=\log_b(m)\cdot\log_a(b)\,

solution Find the value of \log_5(125)\,

solution Find the value of \log_6(216\sqrt{6}),

solution Simplify \log_{0.01}(0.00001)\,

solution Express \frac{3}{2}\log(x)-\frac{1}{3}\log(y)+\frac{2}{3}\log(z)-\frac{1}{5}log(a)\, as a single logarithm.

solution Find the value of \log_3(4)\cdot\log_4(5)\cdot\log_5(6)\cdot\log_6(7)\cdot\log_7(8)\cdot\log_8(9)\,

solution Find the value of \log_3(\sqrt{243})\,

solution Find the value of \log_\sqrt{7}(343)\,

solution Find the value of x if \log_x(4)=\frac{-1}{3}\,

solution Find the value of x if \log_4(x^2+x)-\log_4(x+1)=2\,

solution Find the value of x if \log_2(\log_2(x))=1\,

solution Find the value of x if \log_\sqrt{2}(\log_2(\log_2(x-15))=0\,

solution Find the value of x if \log_2(\log_3(\log_4(x))=1\,

solution Find the value of x if \log_5(x)+\log_x(5)=\frac{5}{2}\,

solution Find the value of x if \log_e(\log_e(\log_e(x)))=0\,

solution Solve \frac{1}{2}\log_{10}(11+4\sqrt{7})=\log_{10}(2+x)\,

solution If \log_x(k)=a\,Then find \log_\frac{1}{x}(k)\, and \log_\frac{1}{x}(\frac{1}{k})\,

solution Simplify \log_{3\sqrt{2}}(5832)\,

solution If \log(a+c)+\log(a-2b+c)=2\log(a-c)\, then show that a,b,c are in Harmonic Progression.

solution If \frac{\log_2(x)}{4}=\frac{\log_2(y)}{6}=\frac{\log_2(z)}{3P},x^3y^2z=1\, then find the value of P.

solution Find the least positive value of x such that\log_{\cos x}\sin x+\log_{\sin x }cos x=2\,

solution Ifa=1+\log_x(yz),b=1+\log_y(zx),c=1+\log_z(xy)\, then show that ab+bc+ca=abc.

solution Ifa^2+b^2=7ab\, then show that 2\log(a+b)=2\log 3+\log a+\log b\,

solution Find the value of x when x^{\log_3(x^2)+(\log_3(x))^{2}-10}=\frac{1}{x^2}\,

solution Solve a^{3-x}\cdot b^{5x}=a^{3x}\cdot b^{x+5}\,

solution Solve \log_2(9^{x-1}+7)=2+\log_2(3^{x-1}+1)\,

solution Solve \log_{16} x+\log_4 x+\log_2 x=7\,

solution Solve (\log_{10}(5\log_{10} 100))^2\,

solution Find x if \log_{10} [98+\sqrt{x^2-12x+36}]=2\,

solution Find the value of \frac{1}{\log_{ab}(abc)}+\frac{1}{\log_{bc}(abc)}+\frac{1}{\log_{ca}(abc)}\,

solution If \frac{\log(\sqrt{x+1}+1)}{\log(\sqrt[3]{x-40})}=3\,Find the value of x

solution What is the value of\log_3(27\cdot\sqrt[4]{9}\cdot\sqrt[3]{9})\,

solution If (3.7)^x=(0.037)^y=10000\, then find the value of 1/x-1/y

solution Find the value of\sqrt{10^{2+\frac{1}{2}\log_{10}(16)}}\,

solution Find the value of\log_{10} \tan(40)\log_{10} \tan(41).......\log_{10} \tan(50)\,

solution Show that \log_3(\log(x^3))-\log_3(\log x)=1\,

solution If \log_{10}(x^2-x-6)=x+\log_{10}(x+2)-4\,,then find the value of x.

solution If \frac{\log x}{2}=\frac{\log y}{3}=\frac{\log z}{5}\, then show that x^4=yz\,

solution Find the value of \log_{\sqrt{a}} \sqrt{a\sqrt{a\sqrt{a\sqrt{a\sqrt{a}}}}}\,

solution Find the value of \log_{\sqrt{2}} \sqrt{2\sqrt{2\sqrt{2\sqrt{2\sqrt{2}}}}}\,

solution If a^x=b^y=c^z=d^w\, Show that\log_a (bcd)=x\cdot(\frac{1}{y}+\frac{1}{z}+\frac{1}{w})\,

solution If a^2+b^2=6ab\, then show that 2\log a+b= \log a+\log b+3\log 2\,

solution Find the value of \frac{\log_9 11}{\log_5 13}-\frac{\log_3 11}{\log_{\sqrt{5}} 13}\,

solution Solve\log_2 x+\log_4 x+\log_{16} x=\frac{21}{4}\,

solution If \frac{\log a}{b-c}=\frac{\log b}{c-a}=\frac{\log c}{a-b}\, prove that a^{b+c}\cdot b^{c+a}\cdot c^{a+b}=1\,

solution Find the value of \log_a a+\log_a (a^2)+\log_a (a^3)+........\log_a (a^{2n-1})\,

solution If \log_{10}(\frac{1}{2^x+x-1})=x(\log_{10}(5)-1)\, then find the value of x.

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