What-are-the-roots-of-the-function-f-x-log-3-x-2log-3-x-2-1-with-x-R-Mastermind-

Question Number 174495 by Mastermind last updated on 02/Aug/22

What are the roots of the function

f (x) = (\log (3^{x}) - 2 \log (3)) \cdot (x^{2} - 1) with

x \in R ?

Mastermind

Commented by kaivan.ahmadi last updated on 02/Aug/22

\pm 1, 2

Commented by Mastermind last updated on 02/Aug/22

your full workings sir!

Answered by Rasheed.Sindhi last updated on 02/Aug/22

f (x) = (\log (3^{x}) - 2 \log (3)) \cdot (x^{2} - 1) = 0

\log (3^{x}) - 2 \log (3) = 0 ∣ x^{2} - 1 = 0

\log (3^{x}) = 2 \log (3) ∣ x^{2} = 1

\log (3^{x}) = \log (3^{2}) ∣ x = \pm 1

3^{x} = 3^{2}

x = 2

Commented by Mastermind last updated on 02/Aug/22

Big thanks to you, {you}^{'} re too much

Answered by Rasheed.Sindhi last updated on 19/Aug/22

A n O t h e r w a y

f (x) = (\log (3^{x}) - 2 \log (3)) \cdot (x^{2} - 1) = 0

(xlog (3) - 2 \log (3)) \cdot (x^{2} - 1) = 0

\log (3) (x - 2) (x - 1) (x + 1) = 0

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

x - 2 = 0 ∣ x - 1 = 0 ∣ x + 1 = 0

x = 2 ∣ x = 1 ∣ x = - 1