How do you solve log_5(3x-1)=log_5 (2x^2) and check the solutions?

1 Answer
Noah G
Dec 18, 2016

x = 1/2 and 1

Explanation:

We start by using the property that if color(magenta)(log_a b = log_a c, then color(magenta)(b = c).

Therefore:

3x - 1 = 2x^2

0 = 2x^2 - 3x + 1

0 = 2x^2 - 2x - x + 1

0 = 2x(x- 1) - 1(x - 1)

0 = (2x- 1)(x - 1)

x = 1/2 and 1

Checking in the original equation, you will find both solutions work. Note that our restrictions on the variable are x > 0, because the log function is undefined in the real number system whenever the value within the logarithm is equal to or smaller than 0. We can automatically confirm both solutions are correct because neither contradict the restriction.

Hopefully this helps!

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