Question

Calcule log64 1/512 = x

Answer 1

$log_{64} \ \frac{1}{512} =x\\ \\\ \ \frac{1}{512}=64^x\\ \\ (\frac{1}{2})^9=(2^6)^x\\ \\ 2^{-9}=2^{6 \cdot x}\\ \\ 2^{-9}=2^{6x}\\ \\-9=6x\\ \\6x=-9\\ \\x= \frac{-9^{:3}}{6_{:3}} \\ \\x= -\frac{3}{2} \\ \\S=\{ -\frac{3}{2} \}$

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$log_{64} \ 512=x\\\\ \ 512=64^x\\ \\2^9=(2^6)^x\\ \\2^9=2^{6\cdot x}\\ \\2^9=2^{6x}\\ \\9=6x\\ \\6x=9\\ \\x= \frac{9^{:3}}{6_{:3}} \\ \\x= \frac{3}{2}\\\\S=\{\frac{3}{2}\}$

Answer 2

Boa Noite!

$log_{64} \frac{1}{512}=x \\ \\ log_{2^6}2^{-9}=x \\ \\ -9. \frac{1}{6} .log_22=x \\ \\ -9. \frac{1}{6}.1=x \\ \\ - \frac{9}{6}=x \\ \\ - \frac{3}{2}=x$

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