Question

2logbase4(x)-logbase4(5)=125

Answer 1

`D:x>0\\\\ 2\log_4x-\log_45=125\\ \log_4x^2-\log_45=\log_44^(125)\\ \log_4(x^2)/(5)=\log_44^(125)\\ (x^2)/(5)=4^(125)\\ x^2=5\cdot4^(125)=5\cdot2^(250)=5\cdot(2^(125))^2\\ x=\sqrt{5\cdot2^(250)} \vee x=-\sqrt{5\cdot2^(250)}\\ x=\sqrt{5\cdot4^(125)} \vee x=-\sqrt{5\cdot4^(125)}\\ x=\sqrt{5\cdot(2^(125))^2} \vee x=-\sqrt{5\cdot(2^(125))^2}\\ x=\sqrt5 \cdot\sqrt{(2^(125))^2} \vee x=-\sqrt5 \cdot\sqrt{(2^(125))^2} \\ x=2^(125)\sqrt5 \vee x=-2^(125)\sqrt5`


`x=-2^(125)\sqrt5 \\ot \in D\Rightarrow \boxed{x=2^(125)\sqrt5}`