Question

Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3

Answer 1

Answer:

x = 1

Step-by-step explanation:

We have to solve the given logarithmic equation of variable x.

The equation is $3\log _{2} (2x) = 3$

⇒ $\log_{2} (2x)^{3} = 3$  

{Since, we know the logarithmic property, $a \log b = \log b^{a}$}

⇒ $\log_{2} (2x)^{3} = 3\log_{2}2 = \log_{2} 2^{3}$

{Since we know that $\log_{a} a = 1$}

Now cancelling log from both sides we get,  

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

⇒ $x^{3} = 1$

⇒ x = 1 (Answer)