The true solution of [tex]\log_2(6x) - \log_2(\sqrt x) = 2[/tex] is x = 4/9
How to determine the solution?
The equation is given as:
[tex]\log_2(6x) - \log_2(\sqrt x) = 2[/tex]
Apply the quotient rule of logarithm
[tex]\log_2(6x/\sqrt x) = 2[/tex]
Rewrite the equation as an exponential equation
[tex]6x/\sqrt x = 2^2[/tex]
Evaluate the square
[tex]6x/\sqrt x = 4[/tex]
Square both sides
[tex]36x^2/x = 16[/tex]
Multiply through by x
[tex]36x^2 = 16x[/tex]
Divide by x
[tex]36x = 16[/tex]
Divide by 36
x = 4/9
Hence, the true solution of [tex]\log_2(6x) - \log_2(\sqrt x) = 2[/tex] is x = 4/9
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