Question

Prove that 1/log base 2 of 4 + 1/log base 8 of 4 + 1/log base 16 of 4 = 4

Answer 1

Answer:

$\frac{1}{ log_{2}(4) } + \frac{1}{ log_{8}(4) } + \frac{1}{ log_{16}(4) } \\ as \: on \: reciprocal \: the \: base \: and \: log \\ \: get \: interchanged \\ log_{4}(2) + log_{4}( 8) + log_{4}( 16 ) \\ log_{4}(2 \times 8 \times 16) \\ log_{4}(256) = log_{4}( {4}^{ 4}) \\ 4 \times log_{4}(4) \: \: \: as \: base \: and \: no \: is \: \\ same \: so \: answer \: is \: one \\ 4 \times 1 = 4$

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