If-4-p-5-Find-2-3p-

Question Number 206473 by hardmath last updated on 15/Apr/24

If 4^{p} = 5

Find : 2^{3 p} = ?

Answered by A5T last updated on 15/Apr/24

2^{2 p} = 5 \Rightarrow 2^{3 p} = \sqrt{125}

p = \frac{{l o g}_{2} 5}{2} \Rightarrow 2^{3 p} = 2^{{l o g}_{2} (5^{\frac{3}{2}})} = 5^{\frac{3}{2}} = \sqrt{125} = 5 \sqrt{5}

Commented by hardmath last updated on 15/Apr/24

thank you very much professor

Answered by Rasheed.Sindhi last updated on 15/Apr/24

2^{3 p} = {(2^{2})}^{\frac{3 p}{2}} = {(4^{p})}^{3 / 2} = 5^{3 / 2} = \sqrt{125} = 5 \sqrt{5}

Answered by BaliramKumar last updated on 16/Apr/24

2^{2 p} = 5 \Rightarrow 2 = 5^{\frac{1}{2 p}}

2^{3 p} = {(5^{\frac{1}{2 p}})}^{3 p} = 5^{\frac{3 p}{2 p}} = 5^{\frac{3}{2}} = 5 \sqrt{5}

Answered by Skabetix last updated on 16/Apr/24

{(2^{2})}^{p} = 5

\Leftrightarrow 2^{2 p} = 5

\Leftrightarrow {(2^{2 p})}^{\frac{3}{2}} = 5^{\frac{3}{2}}

\Leftrightarrow 2^{2 p \times \frac{3}{2}} = 5^{\frac{3}{2}}

\Leftrightarrow 2^{3 p} = 5^{\frac{3}{2}} = 5 \sqrt{5}

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