Question

Find the value of P when 2 ki power 5p divide 2 ki power P equal to 5 under root 2 ki power 2

Answer 1

Step-by-step explanation:

$\frac{ {2}^{5p} }{ {2}^{p} } = 5 \\ or \: {2}^{4p} = 5 \\ taking \: log \: on \: both \: sides \\ 4p log_{2}(2) = log_{2}(5) \\ or \: p = \frac{ log_{2}(5) }{4}$

Answer 2

$\frac{ {2}^{5p} }{ {2}^{p} } = 5 \sqrt{ {2}^{2} } \\ {2}^{4p} = 5 \times 2 = 10 \\ log_{2}( {2}^{4p } ) = log_{2}(10) \\ 4p log_{2}(2) = log_{2}(10) \\ log_{2}(10) = 4p \\ {4p}^{2} = 10 \\ 4p = \sqrt{10} \\ p = \frac{ \sqrt{10} }{4}$

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