o valor de log1/4³² +log 10√10 é:
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Propriedades que utilizarei:

![\sqrt[n]{x^{z}}=x^{z/n} \sqrt[n]{x^{z}}=x^{z/n}](https://tex.z-dn.net/?f=+%5Csqrt%5Bn%5D%7Bx%5E%7Bz%7D%7D%3Dx%5E%7Bz%2Fn%7D+)
![\sqrt{x} = \sqrt[2]{x} \sqrt{x} = \sqrt[2]{x}](https://tex.z-dn.net/?f=+%5Csqrt%7Bx%7D+%3D+%5Csqrt%5B2%5D%7Bx%7D+)



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![log_{(1/4)}32 + log_{(10)}\sqrt{10}=[log_{(2^{-2})}(2^{5})] + [(1 / 2)*log_{(10)}10] log_{(1/4)}32 + log_{(10)}\sqrt{10}=[log_{(2^{-2})}(2^{5})] + [(1 / 2)*log_{(10)}10]](https://tex.z-dn.net/?f=log_%7B%281%2F4%29%7D32+%2B+log_%7B%2810%29%7D%5Csqrt%7B10%7D%3D%5Blog_%7B%282%5E%7B-2%7D%29%7D%282%5E%7B5%7D%29%5D+%2B+%5B%281+%2F+2%29%2Alog_%7B%2810%29%7D10%5D)
![log_{(1/4)}32 + log_{(10)}\sqrt{10}= [(1 / [-2])*log_{(2)}(2^{5})] + [(1 / 2)*1] log_{(1/4)}32 + log_{(10)}\sqrt{10}= [(1 / [-2])*log_{(2)}(2^{5})] + [(1 / 2)*1]](https://tex.z-dn.net/?f=log_%7B%281%2F4%29%7D32+%2B+log_%7B%2810%29%7D%5Csqrt%7B10%7D%3D+%5B%281+%2F+%5B-2%5D%29%2Alog_%7B%282%29%7D%282%5E%7B5%7D%29%5D+%2B+%5B%281+%2F+2%29%2A1%5D)
![log_{(1/4)}32 + log_{(10)}\sqrt{10}=[(- 1 / 2)*5*log_{(2)}2] + (1 / 2) log_{(1/4)}32 + log_{(10)}\sqrt{10}=[(- 1 / 2)*5*log_{(2)}2] + (1 / 2)](https://tex.z-dn.net/?f=log_%7B%281%2F4%29%7D32+%2B+log_%7B%2810%29%7D%5Csqrt%7B10%7D%3D%5B%28-+1+%2F+2%29%2A5%2Alog_%7B%282%29%7D2%5D+%2B+%281+%2F+2%29)
![log_{(1/4)}32 + log_{(10)}\sqrt{10}=[(- 5 / 2)*1] + (1 / 2) log_{(1/4)}32 + log_{(10)}\sqrt{10}=[(- 5 / 2)*1] + (1 / 2)](https://tex.z-dn.net/?f=log_%7B%281%2F4%29%7D32+%2B+log_%7B%2810%29%7D%5Csqrt%7B10%7D%3D%5B%28-+5+%2F+2%29%2A1%5D+%2B+%281+%2F+2%29)




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