Question

Explain the properties and the processes you have to use to solve the following logarithmic equation: log base 3 of x + log base 3 of 4 - 2log base 3 of 3 = 2

Answer 1

Answer:

x = 20.25

Step-by-step explanation:

Given logarithmic equation is  

$\log_{3} x + \log_{3} 4 - 2 \log_{3} 3 = 2$

⇒ $\log_{3} x + \log_{3} 4 - 2  = 2${Since we know the logarithmic property $\log_{a} a = 1$}

⇒ $\log_{3} x + \log_{3} 4 = 4$

⇒ $\log_{3} 4x = 4$ {Since, we know the logarithmic property that $\log_{a} x +\log_{a} y = \log_{a} (xy)$}

⇒ $4x = 3^{4}$ {Converting from logarithm to exponent form}

{Since we know that, if $\log_{b} a = c$ then we can write $a = b^{c}$}

⇒ 4x = 81

⇒ x = 20.25 (Answer)