Question

NEED HELP QUICKLY WILL GIVE RIGHT ANSWER POINTS!!!!

Answer 1

Answer:

$x=45 \sqrt{5}$

Step-by-step explanation:

$2 \log_3x+\log_35=4\log_315$

$\textsf{Apply power log law}\quad n\log_ab=\log_ab^n:$

$\implies \log_3x^2+\log_35=\log_315^4$

$\textsf{Apply product log law}\quad \log_ab+\log_ac=\log_abc:$

$\implies \log_35x^2=\log_315^4$

$\textsf{Apply equality log law}\quad \log_ab=\log_ac \implies b=c:$

$\implies 5x^2=15^4$

$\implies x^2=10125$

$\implies x=\pm \sqrt{10125}$

$\implies x=\pm \sqrt{2025 \cdot 5}$

$\implies x=\pm \sqrt{2025} \sqrt{5}$

$\implies x=\pm 45 \sqrt{5}$

As we cannot take logs of negative numbers,

$\implies x=45 \sqrt{5}\quad \sf only$