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4 years ago

PLEASE HELP ASAP 25 PTS + BRAINLEST TO RIGHT/BEST ANSWER

Mathematics

1 answer:

AlexFokin [52]4 years ago

6 0

Answer:

1.5 = log8(22.627)

Step-by-step explanation:

log4(8) = 1.5

To change base

log a(b)

logc (b)

--------------

logc (a)

Chanding to base 8 we want c =8 (we know a = 4 and b =8)

log8 (8)

----------------

log8 (4)

---------

log8(4)

log8(22.627)

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$f'(x)=\left(\dfrac{20-x}{3x}\right)'=\left(\dfrac{20}{3x}\right)'-\left(\dfrac{x}{3x}\right)'=\dfrac{20}{3}\cdot\left(\dfrac{1}{x}\right)'-\left(\dfrac{1}{3}\right)'=\\\\\\=\dfrac{20}{3}\cdot\left(-\dfrac{1}{x^2}\right)-0=\boxed{-\dfrac{20}{3x^2}}\\\\\\\\f'(x_0)=f'(2)=-\dfrac{20}{3\cdot2^2}=-\dfrac{20}{3\cdot4}=-\dfrac{20}{12}=\boxed{-\frac{5}{3}}$

and the equation of the normal line:

$y-y_0=-\dfrac{1}{f'(x_0)}(x-x_0)\\\\\\y-3=-\dfrac{1}{-\frac{5}{3}}(x-2)\\\\\\y-3=\dfrac{3}{5}(x-2)\\\\\\y-3=\dfrac{3}{5}x-\dfrac{6}{5}\\\\\\y=\dfrac{3}{5}x-\dfrac{6}{5}+3\\\\\\\boxed{y=\dfrac{3}{5}x+\dfrac{9}{5}}$

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