makaunawal5
2022-07-26
Answered

Simplify the following expressions: ${e}^{\mathrm{ln}4+\mathrm{ln}5},{e}^{2\mathrm{ln}5},{\mathrm{log}}_{5}4+{\mathrm{log}}_{5}60-{\mathrm{log}}_{5}7$

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grocbyntza

Answered 2022-07-27
Author has **25** answers

${e}^{\mathrm{ln}4+\mathrm{ln}5}={e}^{\mathrm{ln}20}=20$.

${e}^{2\mathrm{ln}5}=({e}^{\mathrm{ln}5}{)}^{2}={5}^{2}=25$

${\mathrm{log}}_{5}4+{\mathrm{log}}_{5}60-{\mathrm{log}}_{5}7={\mathrm{log}}_{5}(4\ast 60/7)={\mathrm{log}}_{5}(240/7)$

${e}^{2\mathrm{ln}5}=({e}^{\mathrm{ln}5}{)}^{2}={5}^{2}=25$

${\mathrm{log}}_{5}4+{\mathrm{log}}_{5}60-{\mathrm{log}}_{5}7={\mathrm{log}}_{5}(4\ast 60/7)={\mathrm{log}}_{5}(240/7)$

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