If $$\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$$, where x,y and z are positive real numbe

Question

If $$\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$$, where x,y and z are positive real numbers, then the minimum possible value of $$(x+y+z)$$ is

Accepted Answer

48. 64 = 8 2 and 512 = 8 3 64 = 8^2 	ext{and} 512 = 8^3 64 = 8 2 and 512 = 8 3 log ⁡ 64 x 2 + log ⁡ 8 y + 3 log ⁡ 512 ( y z ) = 4 \log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4 lo g 64 ​ x 2 + lo g 8 ​ y ​ + 3 lo g 512 ​ ( y ​ z ) = 4 , Property of log: log ⁡ b m a n = n m log ⁡ b a \lo

If $\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$ , where x,y and z are positive real numbers, then the minimum possible value of $(x+y+z)$ is

If $\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$ , where x,y and z are positive real numbers, then the minimum possible value of $(x+y+z)$ is

If log⁡64x2+log⁡8y+3log⁡512(yz)=4\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4log64​x2+log8​y​+3log512​(y​z)=4, where x,y and z are positive real numbers, then the minimum possible value of (x+y+z)(x+y+z)(x+y+z) is

If log⁡64x2+log⁡8y+3log⁡512(yz)=4\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4log64​x2+log8​y​+3log512​(y​z)=4, where x,y and z are positive real numbers, then the minimum possible value of (x+y+z)(x+y+z)(x+y+z) is

If $\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$ , where x,y and z are positive real numbers, then the minimum possible value of $(x+y+z)$ is

If $\log_{64}{x^{2}+\log_{8}{\sqrt{y}+3\log_{512}{(\sqrt{y}z)}}}=4$ , where x,y and z are positive real numbers, then the minimum possible value of $(x+y+z)$ is