Logarithmic equation

[man111]

If [tex]\log_{12}6=x[/tex] and [tex]\log_{24}54=y[/tex]

Then Calculate [tex]xy+(5x-2y)+4=[/tex]

[martin123456]

[tex]12^x=6,24^y=54[/tex]
[tex]24^{5x}=6^5.2^{5x}[/tex]
[tex]24^{2y}=54^2[/tex]
[tex]24^{5x-2y}=\frac{6^5.2^{5x}}{54^2}[/tex]
[tex]24^{xy}=54^x[/tex]
[tex]24^{xy+5x-2y}=\frac{54^x6^52^{5x}}{54^2}=\frac{6^5}{54^2}2^x2^{5x}3^{3x}=\frac{6^5}{54^2}4^{3x}3^{3x}=\frac{6^5}{54^2}12^{3x}=\frac{6^5}{54^2}6^3=576[/tex]
[tex]\Rightarrow 572[/tex]