${\log }_{a}b=x\iff a^x=b$  

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$\text{a)}{\log }_{7}x=2$  

$7^2=x$  

$x=49$  

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$\text{b)}{\log }_{2}x=-4$  

$2^{-4}=x$  

$x=\frac{1}{16}$  

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$\text{c)}{\log }_{64}x=\frac{1}{3}$  

${64}^{\frac{1}{3}}=x$  

$x=4$  

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$\text{d)}{\log }_{16}x=\frac{5}{4}$  

${16}^{\frac{5}{4}}=x$  

${\left(2^4\right)}^{\frac{5}{4}}=x$  

$x=2^{4\cdot \frac{5}{4}}$  

$x=2^5$  

$x=32$  

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$\text{e)}{\log }_{2\sqrt{2}}x=\frac{4}{3}$  

${\left(2\sqrt{2}\right)}^{\frac{4}{3}}=x$  

$x={\left(2\cdot 2^{\frac{1}{2}}\right)}^{\frac{4}{3}}$  

$x={\left(2^{\frac{3}{2}}\right)}^{\frac{4}{3}}$  

$x=2^{\frac{3}{2}\cdot \frac{4}{3}}$  

$x=2^2$  

$x=4$  

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$\text{f)}{\log }_{\sqrt[3]{3}}x=-1,5$   

${\left(\sqrt[3]{3}\right)}^{-\frac{3}{2}}=x$  

$x={\left(3^{\frac{1}{3}}\right)}^{-\frac{3}{2}}$  

$x=3^{\frac{1}{3}\cdot \left(-\frac{3}{2}\right)}$  

$x=3^{-\frac{1}{2}}$  

$x=\frac{1}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}$  

$x=\frac{\sqrt{3}}{3}$