Desenvolvimento - O valor de log₃ (log₅ (log₂ 2¹²⁵) ) é:
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![\log_3 (\log_5 (log_2 2^{125} )= \log_3 (\log_5 (log_2 2^{125} )=](https://tex.z-dn.net/?f=%5Clog_3+%28%5Clog_5+%28log_2++2%5E%7B125%7D+%29%3D)
![log_3 (\log_5 125)= log_3 (\log_5 125)=](https://tex.z-dn.net/?f=log_3+%28%5Clog_5+125%29%3D)
![\log_3 3=x \log_3 3=x](https://tex.z-dn.net/?f=%5Clog_3+3%3Dx)
![3^x=3 3^x=3](https://tex.z-dn.net/?f=3%5Ex%3D3)
x=1
Veja os calculos
![log_2 2^{125} =x log_2 2^{125} =x](https://tex.z-dn.net/?f=log_2++2%5E%7B125%7D+%3Dx)
![2^x= 2^{125} 2^x= 2^{125}](https://tex.z-dn.net/?f=2%5Ex%3D+2%5E%7B125%7D+)
x=125
![log_5 125=x log_5 125=x](https://tex.z-dn.net/?f=log_5+125%3Dx)
![5^x=5^3 5^x=5^3](https://tex.z-dn.net/?f=5%5Ex%3D5%5E3)
x=3
x=1
Veja os calculos
x=125
x=3
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