Question

1. LOG BASE 27 $\sqrt{3)$ 729 =X

FIND X

Answer 1

value of x = 12/7

your question is ---> $log_{27\sqrt{3}}729=x$ then find value of x .

$log_{27\sqrt{3}}729=x$

729 = 3 × 3 × 3 × 3 × 3 × 3 = 3^6 = (√3)¹²

[ we know, 3 = (√3)² ]

27√3 = 3 × 3 × 3 × √3 = 3³ × √3

= (√3)^6 × √3

= (√3)^7

now, $log_{27\sqrt{3}}729=log_{(\sqrt{3})^7}(\sqrt{3})^{12}$

using logarithmic concept,

• logaⁿ = nloga
• logaⁿ b = 1/n loga b

= $\frac{12}{7}log_{\sqrt{3}}\sqrt{3}$

we also know, $log_aa=1$

so, $log_{\sqrt{3}}\sqrt{3}=1$

so, $\frac{12}{7}log_{\sqrt{3}}\sqrt{3}$ = 12/7

hence, x = 12/7

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