Question

Solve each equation. Round your answers to the nearest ten-thousandth. Please show work. Part 3A​

Answer 1

19.

log9(5x^2 + 10) - log9(10) = 1

<=> log9((5x^2 + 10)/10) = log9(9)

<=> (5x^2 + 10)/10 = 9

<=> 5x^2 + 10 = 90

<=> 5x^2 = 80

<=> x^2 = 16

<=> x = +/- (4)

20.

log5(2x^2 + 4) + log5(3) = 2

<=> log5((2x^2 + 4) x 3) = log3(9)

<=> 6x^2 + 12 = 9

<=> 6x^2 = -3

=> No real x satisfies. ( x^2 always larger or equal to 0)

21.

log6(8) + log6(7 - 2x^2) = 2

<=> log6(8 x (7 - 2x^2)) = log6(36)

<=> 56 - 16x^2 = 36

<=> 16x^2 = 20

<=> x^2 = 5/4

<=> x = +/- sqrt(5/4)

Hope this helps!

:)