Examples -> Algebra -> Logarithm -> Logarithm equations

 Exercise 1. [ID:317] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0] Evaluate the following expression:$\frac{\left({\mathrm{log}}_{\sqrt[3]{27}}\left(3\right)+{\mathrm{log}}_{\sqrt[49]{5}}\left(25\right)\right)×\left({\mathrm{log}}_{\sqrt[4]{81}}\left(9\right)-{\mathrm{log}}_{\sqrt[9]{8}}\left(4\right)\right)}{3+{5}^{\frac{1}{{\mathrm{log}}_{16}\left(25\right)}}×{5}^{{\mathrm{log}}_{5}\left(3\right)}}=\phantom{\rule{0ex}{0ex}}$
 Exercise 2. [ID:318] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0] Evaluate the following expression:$\frac{\left({27}^{\frac{1}{{\mathrm{log}}_{2}\left(3\right)}}+{5}^{{\mathrm{log}}_{25}\left(49\right)}\right)×\left({81}^{\frac{1}{{\mathrm{log}}_{4}\left(9\right)}}-{8}^{{\mathrm{log}}_{4}\left(9\right)}\right)}{3+{5}^{\frac{1}{{\mathrm{log}}_{16}\left(25\right)}}×{5}^{{\mathrm{log}}_{5}\left(9\right)}}=\phantom{\rule{0ex}{0ex}}$
 Exercise 3. [ID:324] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 7] [Number of characters: 0] Evaluate the following expression:${36}^{{\mathrm{log}}_{6}\left(5\right)}+{10}^{1-{\mathrm{log}}_{10}\left(2\right)}-{3}^{{\mathrm{log}}_{9}\left(36\right)}=\phantom{\rule{0ex}{0ex}}$
 Exercise 4. [ID:325] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 8] [Number of characters: 0] Evaluate the following expression:${\mathrm{log}}_{\sqrt{2}}\left(x\right)+{\mathrm{log}}_{2}\left(x\right)+{\mathrm{log}}_{\sqrt{8}}\left(x\right)=11\phantom{\rule{0ex}{0ex}}$
 Exercise 5. [ID:327] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 17] [Number of characters: 0] Evaluate the following expression:${2}^{2{\mathrm{log}}_{10}\left(4x-1\right)}-{7}^{{\mathrm{log}}_{10}\left(4x\right)}={7}^{{\mathrm{log}}_{10}\left(4x-1\right)}-3×{4}^{{\mathrm{log}}_{10}\left(4x\right)}\phantom{\rule{0ex}{0ex}}$
 Exercise 6. [ID:329] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 22] [Number of characters: 87] Evaluate the following expression:${x}^{\frac{{\mathrm{log}}_{10}\left(x+5\right)}{3}}={10}^{5+{\mathrm{log}}_{10}\left(x\right)}\phantom{\rule{0ex}{0ex}}$
 Exercise 7. [ID:330] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 18] [Number of characters: 0] Evaluate the following expression:${\left(\sqrt{x}\right)}^{{\mathrm{log}}_{3}\left(x-1\right)}=3\phantom{\rule{0ex}{0ex}}$
 Exercise 8. [ID:331] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 14] [Number of characters: 0] Evaluate the following expression:${\mathrm{log}}_{x}\left(3\right)+{\mathrm{log}}_{3}\left(x\right)={\mathrm{log}}_{\sqrt{x}}\left(3\right)+{\mathrm{log}}_{3}\left(\sqrt{x}\right)+\frac{1}{2}\phantom{\rule{0ex}{0ex}}$
 Exercise 9. [ID:332] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 9] [Number of characters: 0] Evaluate the following expression:${\mathrm{log}}_{4}\left(x+2\right)×{\mathrm{log}}_{x}\left(2\right)=1\phantom{\rule{0ex}{0ex}}$
 Exercise 10. [ID:333] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 15] [Number of characters: 0] Evaluate the following expression:${x}^{1+{\mathrm{log}}_{10}\left(x\right)}=10x\phantom{\rule{0ex}{0ex}}$
 Exercise 11. [ID:334] [Level: ] [Number of helps: 0] [Number of pictures: 0] [Number of steps: 13] [Number of characters: 242] Solve the following equation: ${\mathrm{log}}_{10}\left({x}^{2}+19\right)-{\mathrm{log}}_{10}\left(x-8\right)=2$