Question

PLEASE HELP ME WITH THESE QUESTIONS

Answer 1

Answer: 8

Explanation:

log₃ (x² - 32) = log₃ (4x) restrictions: x² - 32 > 0 and 4x > 0 ⇒ x > 4√2

x² - 32 = 4x

x² - 4x - 32 = 0

(x - 8)(x + 4) = 0

x - 8 = 0 or x + 4 = 0

x = 8 or x = -4

-4 does not meet the restriction so not valid

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Answer: y = 7x - 6

Explanation:

7x -6

x² + 0x + 4 ) 7x³ - 6x² + 0x + 7

-7x³ + 0x² - 28x

-6x² - 28x + 7

6x² + 0x + 24

-28x + 31

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Answer: x =
`(6)/(5)`

Explanation:

ln 3 + ln x = ln 6 + ln (3x - 3) restrictions: x > 0 and 3x - 3 > 0 ⇒ x > 1

ln (3 * x) = ln (6*(3x - 3))

ln (3x) = ln (18x - 18)

3x = 18x - 18

-18x -18x

-15x = -18

`(-15x)/(-15) = (-18)/(-15)`

x =
`(6)/(5)`

`(6)/(5)` > 1 so answer is valid

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Answer: -5.9761

Explanation:

log ₁₎₂ 63

=
`(log (63))/(log((1)/(2)))`

=
`(1.7993)/(-0.3010)`

= -5.9761