1.
![{\displaystyle x=\log 5^{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/69f27a975f7b5c592ca5b24d426d018fdd60d294)
- Pela multiplicação por constante:
![{\displaystyle x=2\log 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e279002c9e7414fb100dd8ca357c5715193aee07)
- Substituindo log 5 por 0,7:
![{\displaystyle x=2\cdot 0,7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/97255e29de6c3563544de1d61dfd6877e1ad0146)
![{\displaystyle x=1,4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/479a971cdfb2ba4045c14794d344d08f5d382e87)
2.
![{\displaystyle \log 5+\log x=1,7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8466d37c5c37bd10a2bc4946c24f0987f7df3565)
- Substituindo log 5 por 0,7:
![{\displaystyle 0,7+\log x=1,7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91a6540edf5123c948f5c80226f0c0ac2652dd90)
![{\displaystyle \log x=1}](https://wikimedia.org/api/rest_v1/media/math/render/svg/5a4d14075a6f1aa9f40a35e6eb29c60faa179f35)
- Chegamos ao caso da base igual ao logaritmando:
![{\displaystyle 10^{1}=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/6c1c5b21ba95ab73ab288b793cc7ac15d6f92613)
![{\displaystyle x=10}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9dc68280f58d5939fb1cc2d63e7587bf5da1053a)
3.
- Dividindo-se a equação por x:
![{\displaystyle {\frac {\log _{2}5}{\log _{2}10}}={\frac {3,5}{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d140f5cbbfcad6ca1e070b76c7b02935937266ea)
![{\displaystyle \log _{10}5={\frac {3,5}{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee39bd417bb7c719ea726a9cdc0c48a1c383f1ee)
- Substituindo log 5 por 0,7:
![{\displaystyle 0,7={\frac {3,5}{x}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f670c6ec57c1cd0c9d17b5ed82ac52b56d351d01)
![{\displaystyle x={\frac {3,5}{0,7}}=5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9732a428321e2e7852d4244014fbd2206539b6bb)
4.
![{\displaystyle \log x-\log 4=0,7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/869f1d5b6bc393c268854dc6d03abc15ed3f34a0)
- Substituindo 0,7 por log 5:
![{\displaystyle \log x-\log 4=\log 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/66042dda335bd66c15f35ac824791b5aa64b6466)
![{\displaystyle \log {\frac {x}{4}}=\log 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d5055653747d5c765f3f52428d98268da02f88bf)
![{\displaystyle {\frac {x}{4}}=5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/522e2a6aa7b70a8b773d680d817195489ee0c1c8)
![{\displaystyle x=20}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1e665893a76846cafb19376187c796812eeaea02)
5.
![{\displaystyle x=\log _{100}5^{-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d071f3527e6e9e30084e88ed1546264089e3dcf9)
![{\displaystyle x=\log _{10^{2}}5^{-1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/34b5b6952817eece778a775e29396f7608c1e1de)
- Pela multiplicação por constante:
![{\displaystyle x=-2\log 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/76a97750a9291fa9091caa3fdee47a6453748f59)
![{\displaystyle x=-2\cdot 0,7=-1,4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a418d22e64c77fa885181cbc19d9a3e1ec46a45f)
6.
![{\displaystyle \log(0,2\cdot 10)=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/11413a9ebe2d9c30633ced33b3a1f25eccf1dc87)
![{\displaystyle \log 0,2+\log 10=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f43e96ceccd3d2d15bfaf48d1f99a0bed76a800e)
- Temos que log 10 = 1 pelo caso da base igual ao logaritmando:
![{\displaystyle \log 5^{-1}+1=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9273fa09bcab1274431ea21ff55cc5ca568eefed)
- Pela multiplicação por constante:
![{\displaystyle -\log 5+1=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/143f378d34148fdfcd6856dcadf0876b81481403)
![{\displaystyle -0,7+1=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e0e4fbe608f2a51d40c647a0f1201d260878708a)
![{\displaystyle x=0,3}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2f38019d473b0e1452add409d918ac8564cb9e37)
7.
- Pela definição de cologaritmo:
![{\displaystyle x={\frac {(-\log 5)^{2}}{\log 5}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3db9a2c6b601691edbe42fb7a90106665fd0019f)
- Desmembrando o numerador:
![{\displaystyle x={\frac {(-\log 5)(-\log 5)}{\log 5}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/eb4c84f2b8cca6423171d7b177ccb5827f2603e3)
![{\displaystyle x={-(-\log 5)}=\log 5}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1662df3aed2c98b824a9f5441a7efbf0ad6b9d3c)
![{\displaystyle x=0,7}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0938ebe898be0c9b2b9c0c7d7aab128d7967725e)
8.
- Pela definição de cologaritmo:
![{\displaystyle (-\log 5)^{x}=(-\log 2)^{x}-0,4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/618b733b4534ba5272766b5940e338a47782a85f)
- Descobrimos no item 6 da questão 5 que log 2 = 0,3
![{\displaystyle (-0,7)^{x}=(-0,3)^{x}-0,4}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2bbc9df9f09a4bb8f68b5fb41675674360b88c6f)
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