Question

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

Answer 1

`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`