EXERCICES
- Traduire en logarithmes les expressions :
![{\displaystyle {\begin{array}{ll}958.&{\rm {x=ab\ ;\quad x=a^{2}b\ ;\quad x=a^{3}b^{3}\ ;\quad x=a(b+c).}}\\959.&{\rm {x={\cfrac {ab}{c}}\ ;\quad x={\cfrac {a^{3}}{bc}}\ ;\quad x={\cfrac {b^{2}}{a^{3}c}}\ ;\quad x={\cfrac {a(1+r)}{r}}.}}\\960.&{\rm {x={\sqrt[{3}]{a}}\ ;\quad x={\sqrt {ab}}\ ;\quad x={\sqrt[{5}]{a^{2}b^{3}}}\ ;\quad x={\sqrt {a^{2}-b^{2}}}.}}\\961.&{\rm {x=(1+r)^{n}\ ;\quad x=a\left[(1+r)^{n}-1\right]\ ;\quad x=Dr(1+r)^{n}.}}\\962.&{\rm {A={\cfrac {a\left[(1+r)^{n}-1\right]}{r}}\ ;\quad A={\cfrac {a(1+r)\left[(1+r)^{n}-1\right]}{r}}.}}\\963.&{\rm {D(1+r)^{n}={\cfrac {a\left[(1+r)^{n}-1\right]}{r}}\ ;\quad a={\cfrac {D(1+r)^{n}}{(1+r)^{n}-1}}}}\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9d3e5a647d7911cea584d6dae1d324d31a635bb0)
– Inversement, rétablir les expressions qui ont pour logarithmes :
![{\displaystyle {\begin{array}{ll}964.&\log \mathrm {a} +\log \mathrm {b} \ ;\quad \log \mathrm {x} -\log \mathrm {y} \ ;\quad 3\,\log \mathrm {x} +2\,\log \mathrm {y} .\\965.&\log {\sqrt {\mathrm {a} }}+\log {\sqrt {\mathrm {b} }}\ ;\quad 2\,\log \mathrm {x} -{\cfrac {\log \mathrm {y} }{3}}\ ;\quad \log(\mathrm {a+b} )-\log(\mathrm {a-b} ).\\966.&3\,\log(6\mathrm {x} -4)+3\log(2\mathrm {x} +5)\ ;\quad {\cfrac {1}{2}}\left[\log \mathrm {\left(a^{2}-b^{2}\right)} -\log(\mathrm {a-b} )\right].\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/82c60a5624dafefa9d141266286407d4eb0893f2)
– Trouver les logarithmes des nombres :
![{\displaystyle {\begin{array}{ll}967.&8\ ;\quad 25\ ;\quad 104\ ;\quad 360\ ;\quad 1035\ ;\quad 81350\ ;\quad 75246.\\968.&1{,}05\ ;\quad 8{,}75\ ;\quad 3{,}1416\ ;\quad 0{,}82\ ;\quad 0{,}025\ ;\quad 308{,}75.\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cb784cfd9d2650bf769cc796e620eec82bf744d8)
– Trouver les nombres qui ont pour logarithmes :
![{\displaystyle {\begin{array}{ll}969.&0{,}15229\ ;\quad 3{,}66049\ ;\quad {\overline {1}}{,}92454\ ;\quad 2{,}00561\ ;\quad {\overline {2}}{,}65600.\\970.&0{,}63565\ ;\quad 4{,}99010\ ;\quad {\overline {3}}{,}41390\ ;\quad 0{,}06215\ ;\quad {\overline {1}}{,}33208.\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b8e7fb35194c5f005d2220778e92b86b20567df5)
– Calculer par logarithmes :
![{\displaystyle {\begin{array}{ll}971.&(1{,}04)^{12}\ ;\quad (1+0{,}043)^{18}\ ;\quad {\sqrt {2}}\ ;\quad {\sqrt[{3}]{4}}\ ;\quad {\sqrt {\cfrac {1}{\pi }}}.\\972.&500\left[1{,}03^{8}-1\right]\ ;\quad 4200\times 1{,}035^{15}\ ;\quad {\sqrt[{3}]{2}}\ ;\quad {\sqrt {3}}\ ;\quad {\sqrt {\pi }}\ ;\quad {\sqrt[{3}]{\pi }}\\973.&{\cfrac {300\times 1{,}04\left(1{,}04^{20}-1\right)}{0{,}04}}\ ;\quad 54{\sqrt[{3}]{\cfrac {1}{\pi }}}\ ;\quad \left({\sqrt[{5}]{35412}}\right)^{2}.\\974.&{\sqrt {0{,}0225}}\ ;\quad {\sqrt {1000}}\ ;\quad {\sqrt {0{,}4}}\ ;\quad {\sqrt[{3}]{0{,}27}}\ ;\quad {\sqrt[{3}]{0{,}064}}.\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38b6557bef3565c5eda767c4e62763ca803f4795)
![{\displaystyle 975.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ae432aa3459b5854e9e7c3ffd97f98b60406a38a)
– Étant donnés
![{\displaystyle \log 2=0{,}30103}](https://wikimedia.org/api/rest_v1/media/math/render/svg/643ca8fc1f46138b3d25fd4d65a6e8eab0ccf344)
et
![{\displaystyle \log 5=0{,}69897,}](https://wikimedia.org/api/rest_v1/media/math/render/svg/60a3756b5da927052e88cea5c0858146c25b97e5)
trouver sans la table
![{\displaystyle \log 4,\,\log 8,\,\log 25,\,\log 125,\,\log 20,\,\log 50,\,\log 40.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9797fa4ccfe390d77b430f4c2563ade0e7fcdebd)
![{\displaystyle 976.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a62b341a0c1b17835653e54957ff0859249e7f90)
– La somme de deux nombres est
![{\displaystyle 254\,;}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b99b3d801727c056ed5f51a0a68958783cb0ed48)
la somme de leurs logarithmes est
![{\displaystyle 3.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d75e17f7e7094c457fa7c8f743c3d8622eebd8ef)
Trouver ces nombres, sans l’aide des tables.
– Résoudre les équations :
![{\displaystyle {\begin{array}{ll}977.&\log(3x-12)+\log(6x+3)=\log 96.\\978.&8\log \left({\cfrac {\mathrm {x} }{4}}\right)-2\log \left({\cfrac {\mathrm {x} }{6}}\right)=3\log \mathrm {x} -4\log 4.\end{array}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b26197cf4fdd48ecea583dd175a782dabc1f7f7a)
![{\displaystyle 979.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5855dc8c6f02ee4eb31797e1746ba0dbf502042)
– Quelle est la hauteur du double litre en étain ?
![{\displaystyle 980.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/54087486460f2c7f1fa4c4bb634b8439eead13c1)
– Quel est le diamètre d’un aérostat sphérique dont la capacité es
![{\displaystyle 1200^{{\text{m}}^{3}}\ ?}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffae9656c3b82b6386dcf7815ff93a463a22dca)