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

Question 1

Question 2

Answer:

x=45 √(5)

Explanation:

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

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

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

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

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

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

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

$\implies x^2=10125$

$\implies x=\pm √(10125)$

$\implies x=\pm √(2025 \cdot 5)$

$\implies x=\pm √(2025) √(5)$

$\implies x=\pm 45 √(5)$

As we cannot take logs of negative numbers,

$\implies x=45 √(5)\quad \sf only$

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