Evaluate $\log_{2}{\log_{3}{\log_{5}{(125)^3}}}$

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d

Find the Log of 125 cube to the base 5

$=\,\,$ $\log_{2}{\log_{3}{\log_{5}{(5 \times 5 \times 5)^3}}}$

$=\,\,$ $\log_{2}{\log_{3}{\log_{5}{(5^3)^3}}}$

$=\,\,$ $\log_{2}{\log_{3}{\log_{5}{5^{3 \times 3}}}}$

$=\,\,$ $\log_{2}{\log_{3}{\log_{5}{5^9}}}$

$=\,\,$ $\log_{2}{\log_{3}{(9 \times \log_{5}{5})}}$

$=\,\,$ $\log_{2}{\log_{3}{(9 \times 1)}}$

$=\,\,$ $\log_{2}{\log_{3}{(9)}}$

Find the Log of 9 cube to the base 3

$=\,\,$ $\log_{2}{\log_{3}{(3 \times 3)}}$

$=\,\,$ $\log_{2}{\log_{3}{(3^2)}}$

$=\,\,$ $\log_{2}{\log_{3}{3^2}}$

$=\,\,$ $\log_{2}{(2 \times \log_{3}{3})}$

$=\,\,$ $\log_{2}{(2 \times 1)}$

$=\,\,$ $\log_{2}{(2)}$

Find the Log of 2 cube to the base 2

$=\,\,$ $\log_{2}{2}$

$=\,\,$ $1$

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