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 = [tex]\frac{6}{5}[/tex]
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
[tex]\frac{-15x}{-15} = \frac{-18}{-15}[/tex]
x = [tex]\frac{6}{5}[/tex]
[tex]\frac{6}{5}[/tex] > 1 so answer is valid
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Answer: -5.9761
Step-by-step explanation:
log ₁₎₂ 63
= [tex]\frac{log (63)}{log(\frac{1}{2})}[/tex]
= [tex]\frac{1.7993}{-0.3010}[/tex]
= -5.9761
