Find value of 1log 5 3

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Find value of $\frac{1}{{log}_{5} 3}$

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x

{log}_{5} \sqrt[3]{5} = x

If $x = 1 + l o g 2 - l o g 5, y = 2 l o g 3$ and $z = l o g a - l o g 5$ ; find the value of a, if $x + y = 2 z$ .

\frac{2}{{log}_{4} {(2000)}^{6}} + \frac{3}{{log}_{5} {(2000)}^{6}}

x = 4 {log}_{5} 2 + {log}_{5} sin \frac{π}{5} + {log}_{5} sin \frac{2 π}{5} + {log}_{5} sin \frac{3 π}{5} + {log}_{5} sin \frac{4 π}{5}

1

sin 18^{o} = \frac{1}{4} (\sqrt{5} - 1)

cos 36^{o} = \frac{1}{4} (\sqrt{5} + 1)

{log}_{5} 125

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