Algebra-Functions

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Exponential

solution {\frac  {1}{1\cdot 2}}-{\frac  {1}{2\cdot 3}}+{\frac  {1}{3\cdot 4}}-{\frac  {1}{4\cdot 5}}+........\,

solution Show that {\frac  {1\cdot 2}{1!}}+{\frac  {2\cdot 3}{2!}}+{\frac  {3\cdot 4}{3!}}+...........=3e\,

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

solution Find the sum of the infinite series {\frac  {1}{1\cdot 3}}+{\frac  {1}{2}}[{\frac  {1}{3\cdot 5}}]+{\frac  {1}{3}}[{\frac  {1}{5\cdot 7}}].........\,

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^{3}y^{2}z=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}}cosx=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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