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Marrrta [24]
3 years ago
12

Solve the equation:2logx-log(x-2)=2log3​

Mathematics
1 answer:
andriy [413]3 years ago
4 0

Answer:

x=6   x=3

Step-by-step explanation:

2logx-log(x-2)=2log3​

We know that a log b = log b^a

logx^2-log(x-2)=log3^2​

logx^2-log(x-2)=log9

subtract log 9 from each side

logx^2-log(x-2)-log9=0

We know that log a - log b = log (a/b)

log(x^2/9(x-2))=0

Raise each side to the power of 10   to get rid of the log

10 ^log(x^2/9(x-2))= 10 ^0

10^ log cancels and 10^0 =1

(x^2/9(x-2))=1

Multiply each side by 9(x-2)

x^2 =9(x-2)

Subtract 9(x-2) from each side

x^2 - 9(x-2) = 9(x-2) - 9(x-2)

x^2 - 9(x-2) = 0

Distribute

x^2 - 9x +18 = 0

Factor

(x-6) (x-3) =0

Using the zero product property

x-6 =0    x-3 =0

x=6   x=3

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find the nearest two positive coterminal angles and the nearest two negative coterminal angles for 420°
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Negative Coterminal Angles = -300°, -660°

Step-by-step explanation:

<h3>Positive Coterminal Angles:</h3>

To find nearest two coterminal angle of 420°:

1) Subtract 360° from 420°:

420°- 360° = 60° (First Positive Coterminal Angle)

2)Add 360° to 420°:

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<h3>Negative Coterminal angles:</h3>

To find nearest two negative coterminal angles of 420°. We' lave to take the value below 0.

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