Log64 base 2 + log243 base 3
Soluções para a tarefa
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Boa tarde Rafaéla!
Solução!
O objetivo da resolução desse tipo de logaritmo(definição) tem que decompor o logaritmando em fatores primos para ficar igual a base.
Vamos resolver fazendo separadamente e no final somamos os resultados.
![64|2\\
32|2\\
16|2\\
~~8|2\\
~~4|2\\
~~2|2\\
~~1\\\\2^{6}\\\\\\\
log_{2}64\\\\
log_{2}64=x\\\\
2^{x}=2^{6}\\\\
x=6](https://tex.z-dn.net/?f=64%7C2%5C%5C%0A32%7C2%5C%5C%0A16%7C2%5C%5C%0A+%7E%7E8%7C2%5C%5C%0A+%7E%7E4%7C2%5C%5C%0A+%7E%7E2%7C2%5C%5C%0A+%7E%7E1%5C%5C%5C%5C2%5E%7B6%7D%5C%5C%5C%5C%5C%5C%5C%0Alog_%7B2%7D64%5C%5C%5C%5C%0Alog_%7B2%7D64%3Dx%5C%5C%5C%5C%0A2%5E%7Bx%7D%3D2%5E%7B6%7D%5C%5C%5C%5C%0Ax%3D6++++%0A%0A "64|2\\
32|2\\
16|2\\
~~8|2\\
~~4|2\\
~~2|2\\
~~1\\\\2^{6}\\\\\\\
log_{2}64\\\\
log_{2}64=x\\\\
2^{x}=2^{6}\\\\
x=6")
![243|3\\
~~81|3\\
~~27|3\\
~~~9|3\\
~~~3|3\\
~~~1\\\\
3^{5} \\\\\\\
log_{3}243\\\\
log_{3}243=x\\\\
3^{x}=3^{5} \\\\\
x=5](https://tex.z-dn.net/?f=243%7C3%5C%5C%0A++%7E%7E81%7C3%5C%5C%0A++%7E%7E27%7C3%5C%5C%0A+++%7E%7E%7E9%7C3%5C%5C%0A+++%7E%7E%7E3%7C3%5C%5C%0A+++%7E%7E%7E1%5C%5C%5C%5C%0A3%5E%7B5%7D+%5C%5C%5C%5C%5C%5C%5C%0Alog_%7B3%7D243%5C%5C%5C%5C%0Alog_%7B3%7D243%3Dx%5C%5C%5C%5C%0A3%5E%7Bx%7D%3D3%5E%7B5%7D+%5C%5C%5C%5C%5C%0Ax%3D5+ "243|3\\
~~81|3\\
~~27|3\\
~~~9|3\\
~~~3|3\\
~~~1\\\\
3^{5} \\\\\\\
log_{3}243\\\\
log_{3}243=x\\\\
3^{x}=3^{5} \\\\\
x=5")
Então!
![log_{2}64+log_{3}243 \\\\\
~~~~~~6+5=11](https://tex.z-dn.net/?f=log_%7B2%7D64%2Blog_%7B3%7D243+%5C%5C%5C%5C%5C%0A%7E%7E%7E%7E%7E%7E6%2B5%3D11 "log_{2}64+log_{3}243 \\\\\
~~~~~~6+5=11")
Boa tarde!
Bons estudos!
Solução!
O objetivo da resolução desse tipo de logaritmo(definição) tem que decompor o logaritmando em fatores primos para ficar igual a base.
Vamos resolver fazendo separadamente e no final somamos os resultados.
Então!
Boa tarde!
Bons estudos!
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