2 years ago

Express ln3+2lnx as a single logarithm

Mathematics

1 answer:

Naily [24]2 years ago

4 0

Answer:

ln (3x^2)

Step-by-step explanation:

ln3 + 2ln(x)

= ln3 + ln(x^2)

= ln (3x^2)

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For the given equation, find the values of a, b, and c, determine the direction in which

Shkiper50 [21]

Answer: Table D

Step-by-step explanation:

The coefficient of x^2 is -9, the coefficient of x is 7, and the constant is 0, so we know a = -9, b = 7, c = 0.

This eliminates tables A, B, and C.

Thus, table D is the answer.

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2 years ago

Find a and b so that f(x) = x^3 + ax^2 + b will have a critical point at (2,3).

Digiron [165]

Using the critical point concept, it is found that a = -3 and b = 7.

<h3>What are the critical points of a function?</h3>

The critical points of a function are the values of x for which:

$f^{\prime}(x) = 0$

In this problem, the function is:

$f(x) = x^3 + ax^2 + b$

Hence, the derivative is:

$f^{\prime}(x) = 3x^2 + 2ax$

Then:

$f^{\prime}(x) = 0$

$3x^2 + 2ax = 0$

$x(3x + 2a) = 0$

$x = 0$

$3x + 2a = 0$

$3x = -2a$

$x = -\frac{2a}{3}$

Since the critical point is at x = 2, we have that:

$-\frac{2a}{3} = 2$

$-2a = 6$

$2a = -6$

$a = -3$

Then:

$f(x) = x^3 - 3x^2 + b$

Critical point at (2,3) means that when $x = 2, y = 3$ , then:

$3 = 2^3 - 3(2)^2 + b$

$8 - 12 + b = 3$

$b = 7$

You can learn more about the critical point concept at brainly.com/question/2256078

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1 year ago

Teresa graphs the following 3 equations: y=2^x, y=x^2+2, and y=2x^2. She says that the graph of y=2^x will eventually surpass bo

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3 years ago

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Please help ASAP!<br> 3(T + 4) - 2(2T + 3) = -4 <br> Thank You!

kakasveta [241]

The answer would be t=10

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3 years ago

How did you decide which make a ten fact to use? Explain

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3 years ago