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
Accepted Solution
A:
Answer:x = 20.25Step-by-step explanation:Given logarithmic equation is [tex]\log_{3} x + \log_{3} 4 - 2 \log_{3} 3 = 2[/tex]
⇒ [tex]\log_{3} x + \log_{3} 4 - 2 = 2[/tex]{Since we know the logarithmic property [tex]\log_{a} a = 1[/tex]}
⇒ [tex]\log_{3} x + \log_{3} 4 = 4[/tex]
⇒ [tex]\log_{3} 4x = 4[/tex] {Since, we know the logarithmic property that [tex]\log_{a} x +\log_{a} y = \log_{a} (xy)[/tex]}
⇒ [tex]4x = 3^{4}[/tex] {Converting from logarithm to exponent form}
{Since we know that, if [tex]\log_{b} a = c[/tex] then we can write [tex]a = b^{c}[/tex]}
⇒ 4x = 81
⇒ x = 20.25 (Answer)