Question

What is the true solution to the logarithmic equation below?

Answer 1

Answer:

x = 4/9

C

Step-by-step explanation:

log_2(6x/) - log_2(x^(1/2) = 2         Given

log_2(6x/x^1/2) = 2                         Subtracting logs means division

log_2(6 x^(1 - 1/2)) = 2                     Subtract powers on the x s

log_2(6 x^(1/2) ) = 2                         Take the anti log of both sides

6 x^1/2 = 2^2                                    Combine the right

6 x^1/2 = 4                                        Divide by 6  

x^1/2 = 4/6 = 2/3                               which gives 2/3 now square both sides

x = (2/3)^2                                      

x = 4/9

Answer 2

Answer:

Option c

Step-by-step explanation:

The given logarithmic equation is

$log_{2} (6x)-log_{2}(\sqrt{x})=2$

$log_{2}[\frac{(6x)}{\sqrt{x}}]=2$ [since log$(\frac{a}{b})$= log a - log b]

$log_{2}[\frac{(6\sqrt{x})\times\sqrt{x}}{\sqrt{x}}]=2$ [since x = $(\sqrt{x})(\sqrt{x})$]

$log_{2}(6\sqrt{x} )=2$

$6\sqrt{x} =2^2$  [logₐ b = c then $a^{c}=b$

$6\sqrt{x} =4$

$\sqrt{x} =\frac{4}{6}$

$\sqrt{x} =\frac{2}{3}$

$x=(\frac{2}{3})^2$

        = $\frac{4}{9}$

Option c is the answer.