Question
Solve for $\mathbf{x}, \log _x^{15 \sqrt{5 } }=2-\log _x^{3 \sqrt{ 5} }$
✓
Answer
$\log_x 15\sqrt 5 = 2 - \log_x3\sqrt 5$
$\Rightarrow \log_x15\sqrt 5 + \log_x3\sqrt 5 = 2$
$\Rightarrow \log_x( 15\sqrt 5 \times 3\sqrt 5 ) = 2$
$\Rightarrow \log_x225 = 2$
$\Rightarrow \log_x15^2 = 2$
$\Rightarrow 2 \log_x15= 2$
$\Rightarrow \log_x15 = 1$
$\Rightarrow x = 15.$
$\Rightarrow \log_x15\sqrt 5 + \log_x3\sqrt 5 = 2$
$\Rightarrow \log_x( 15\sqrt 5 \times 3\sqrt 5 ) = 2$
$\Rightarrow \log_x225 = 2$
$\Rightarrow \log_x15^2 = 2$
$\Rightarrow 2 \log_x15= 2$
$\Rightarrow \log_x15 = 1$
$\Rightarrow x = 15.$
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