Question

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$\bf log_a ^3\sqrt{x^7y^8 \div 4 \sqrt{z} }$
NO FOR JUNIOR'S -,-
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Answer 1

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$\bf log_a ^3\sqrt{x^7y^8 \div 4 \sqrt{z} }$

Consider,

$Log_a \: ³√x⁷y⁸ ÷ ⁴√z$

$Log_a ³√x⁷y⁸ ÷ ⁴√z = Log_a(³√x⁷y⁸/ ⁴√z)$

$→ Log_a(x⁷y⁸/ ⁴√z)⅓$

$→ 1/3Log_a(x⁷y⁸/ ⁴√z)$

$→ 1/3{Log_a(x⁷y⁸) - Log_a(⁴√z)}$

$→ 1/3{Log_a(x⁷y⁸) - Log_a(z)¼}$

$→ 1/3{Log_a(x⁷y⁸) - 1/4Log_a(z)}$

$→ 1/3{Log_a(x⁷) + Log_a(x⁸) - 1/4Log_a(z)}$

Now,

$→ Log_a ³√x⁷y⁸ ÷ ⁴√z$

$= 1/2{7Log_a(x) + 8Log_a(y) - 1/4Log_a(z)}$

By Vikramjeeth