Category: Logarithms

Question Number 209991 by efronzo1 last updated on 28/Jul/24 $$\frac{{10}^{\log {}_3\left(6\right)}.{15}^{\log {}_3\left(\frac{2}{3}\right)}}{6^{\log {}_3\left(\frac{2}{3}\right)}.5^{\log {}_3\left(\frac{4}{3}\right)}}=?$$ Answered by Rasheed.Sindhi last updated…

Question Number 208412 by efronzo1 last updated on 15/Jun/24 Answered by A5T last updated on 15/Jun/24 $$8={24}^{\frac{1}{a}},27={24}^{\frac{1}{b}},64={24}^{\frac{1}{c}}$$$$\Rightarrow {24}^3=8\times 27\times 64={24}^{(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{ab+bc+ca}{abc})}$$$$\Rightarrow\frac{{ab}+{bc}+{ca}}{{abc}}=\mathrm{3}\Rightarrow\frac{\mathrm{2022}{abc}}{{ab}+{bc}+{ca}}=\mathrm{2022}×\frac{\mathrm{1}}{\mathrm{3}}=\mathrm{674} \…

Question Number 208322 by alcohol last updated on 11/Jun/24 Answered by Berbere last updated on 11/Jun/24 $$\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\left(\mathrm{1}+\frac{\mathrm{1}}{{k}}\right)^{{k}} =\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}} {\prod}}\frac{\left(\mathrm{1}+{k}\right)^{{k}} }{{k}^{{k}} }=\underset{{k}=\mathrm{1}} {\overset{{n}−\mathrm{1}}…

Question Number 208083 by nachosam last updated on 04/Jun/24 $${\int }_{[0,\mathrm{\infty }]}{\left(\frac{1}{x}\right)}^{ln\left(x\right)}dx$$$$$$ Answered by Saiki last updated on 04/Jun/24 Answered by…

Question Number 205496 by cortano12 last updated on 22/Mar/24 Answered by Frix last updated on 22/Mar/24 $$x>0$$$$t=\sqrt[3]{x}$$$${\log }_2(1+t)={3\log }_{7}x$$$$\mathrm{Obviously}\:{t}=\mathrm{7}…