Question

PLEASE HELP ME WITH THESE QUESTIONS

Answer 1

Answer: 8

Step-by-step 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

Step-by-step 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 = $\frac{6}{5}$

Step-by-step 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

$\frac{-15x}{-15} = \frac{-18}{-15}$

x = $\frac{6}{5}$

     $\frac{6}{5}$ > 1 so answer is valid

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Answer:  -5.9761

Step-by-step explanation:

log ₁₎₂ 63

= $\frac{log (63)}{log(\frac{1}{2})}$

= $\frac{1.7993}{-0.3010}$

= -5.9761