How do you solve $\frac{1}{2} {log}_{6} (16 x) = 3$ $1/2log_6(16x)=3$ ?

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Answer 1 · 2016-08-11T19:59:01

$x = 2916$ $x=2916$ .

$\frac{1}{2} {log}_{2} (16 x) = 3$ $1/2log_2(16x)=3$

$\Rightarrow {log}_{6} (16 x) = 6$ $rArr log_6(16x)=6$

$\Rightarrow 16 x = 6^{6} = 2^{6} \cdot 3^{6}$ $rArr 16x=6^6=2^6*3^6$

$\Rightarrow x = \frac{2^{6} \cdot 3^{6}}{16} = \frac{2^{6} \cdot 3^{6}}{2^{4}} = 2^{2} \cdot 3^{6}$ $rArr x=(2^6*3^6)/16=(2^6*3^6)/2^4=2^2*3^6$

$\Rightarrow x = 4 \cdot 729 = 2916$ $rArr x=4*729=2916$ .

How do you solve 12log6(16x)=31/2log_6(16x)=3?