Question

Kuis (No. 150)
[tex]\huge\boxed{2^{\sqrt[3]{p}}=4^{\sqrt[4]{p}}}[/tex]
p = {..., ...}

Answer 1

eksponen

2^(³√p) = 4^(⁴√p)

2^(³√p) = 2^(2 ⁴√p)

³√p = 2 ⁴√p

kedua ruas dipangkatkan 12

p⁴ = 2¹² p³

p³(p - 2¹²) = 0

p = 0 atau p = 2¹² = 4096

p = {0 , 4096}

Answer 2

Verified answer

Jawaban:

p = {0, 4096}

Penjelasan dengan langkah-langkah:

[tex]2 {}^{ \sqrt[3]{p} } = {2}^{2 \sqrt[4]{p} } [/tex]

[tex] \sqrt[3]{p} = 2 \sqrt[4]{p} [/tex]

[tex] \sqrt[3]{p} {}^{12} = (2 \sqrt[4]{p} ) {}^{12} [/tex]

[tex] {p}^{4} = 4096p {}^{3} [/tex]

[tex]p {}^{4} - 4096p {}^{3} = 0[/tex]

[tex] {p}^{3} \times (p - 4096) = 0[/tex]

[tex] {p}^{3 } = 0 \\ p - 4096 = 0[/tex]

[tex]p = 0 \\ p = 4096[/tex]

[tex]p1 = 0 \:, p2 = 4096[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alfat}}[/tex]