Question

Find the values of x such that: 2 log3^x - log3^(x - 2) - 2 = 0

Plz solve it Step by step

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Answer 1

Answer:

How do I solve the following question. 'Find the values of x such that 2log3(x) - log3(x-2) = 2'.To simplify this equation in order to solve it, the first step is to simplify the 2log3x term. The log rule 'n.logb(m) = logb(m)n' will enable us to do this. Using this rule makes the equation: log3(x2) - log3(x-2) = 2. The next step is to recognise that the equation can be simplified by using another log rule 'logb(m) - logb(n) = logb(m/n)'. So by applying this rule to our equation we end up with log3(x2/(x-2)) = 2. Our equation is now made up of just two terms. Logarithms are just another way of writing indices. If a = bcthen c = logba . In our equation a = (x2/(x-2)), b = 3 and c = 2, by substituting these values into a = bc, you get (x2/(x-2)) = 32.Now this expression can be rearranged into a quadratic equation, which can then be solved. The steps for this are shown below:(x2/(x-2)) = 9 x2 = 9(x-2) x2= 9x -18 x2- 9x + 18 = 0 x2- 9x +18 = 0 (x-6)(x-3)=0 x=3, x=6

Step-by-step explanation:

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