All categories

2 years ago

Solve the equation for x. show your work log(2x-6)=2

Mathematics

2 answers:

borishaifa [10]2 years ago

8 0

Answer:

x = e^2/2 + 3

Step-by-step explanation:

Solve for x:

log(2 x - 6) = 2

Hint: | Eliminate the logarithm from the left hand side.

Cancel logarithms by taking exp of both sides:

2 x - 6 = e^2

Hint: | Isolate terms with x to the left hand side.

Add 6 to both sides:

2 x = e^2 + 6

Hint: | Solve for x.

Divide both sides by 2:

Answer: x = e^2/2 + 3

Mrac [35]2 years ago

8 0

Answer:

x = 53

Step-by-step explanation:

Rewrite log ( 2 x − 6 ) = 2 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b ≠ 1 , then log b ( x ) = y is equivalent to b y = x .

10 = x − 6

Solve for x .

Rewrite the equation as

x − 6 = 10 .

x − 6 = 10

Raise 10 to the power of 2 .

x − 6 = 100

Move all terms not containing x to the right side of the equation.

x = 106

Divide each term by 2 and simplify. x = 53

You might be interested in

Find a cubic function with the given zeros.

Fed [463]

Answer:

The correct option is D) $f(x) = x^3 + 2x^2 - 2x - 4$ .

Step-by-step explanation:

Consider the provided cubic function.

We need to find the equation having zeros: Square root of two, negative Square root of two, and -2.

A "zero" of a given function is an input value that produces an output of 0.

Substitute the value of zeros in the provided options to check.

Substitute x=-2 in $f(x) = x^3 + 2x^2 - 2x + 4$ .

$f(x) = x^3 + 2x^2 - 2x + 4\\f(x) = (-2)^3 + 2(-2)^2 - 2(-2) + 4\\f(x) =-8 + 2(4)+4 + 4\\f(x) =8$

Therefore, the option is incorrect.

Substitute x=-2 in $f(x) = x^3 + 2x^2 + 2x - 4$ .

$f(x) = x^3 + 2x^2 + 2x - 4\\f(x) = (-2)^3 + 2(-2)^2 + 2(-2) - 4\\f(x) =-8+2(4)-4-4\\f(x) =-8$

Therefore, the option is incorrect.

Substitute x=-2 in $f(x) = x^3 - 2x^2 - 2x - 4$ .

$f(x) = x^3 - 2x^2 - 2x - 4\\f(x) = (-2)^3 - 2(-2)^2 - 2(-2) - 4\\f(x) =-8-8+4-4\\f(x) =-16$

Therefore, the option is incorrect.

Substitute x=-2 in $f(x) = x^3 + 2x^2 - 2x - 4$ .

$f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (-2)^3+2(-2)^2 - 2(-2) - 4\\f(x) =-8+8+4-4\\f(x) =0$

Now check for other roots as well.

Substitute x=√2 in $f(x) = x^3 + 2x^2 - 2x - 4$ .

$f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (\sqrt{2})^3+2(\sqrt{2})^2 - 2(\sqrt{2}) - 4\\f(x) =2\sqrt{2}+4-2\sqrt{2}-4\\f(x) =0$

Substitute x=-√2 in $f(x) = x^3 + 2x^2 - 2x - 4$ .

$f(x) = x^3 + 2x^2 - 2x - 4\\f(x) = (-\sqrt{2})^3+2(-\sqrt{2})^2 - 2(-\sqrt{2}) - 4\\f(x) =-2\sqrt{2}+4+2\sqrt{2}-4\\f(x) =0$

Therefore, the option is correct.

8 0

3 years ago

A roller coaster climbs 180 feet above ground level then drops 60 feet .How far above ground level is the roller coaster?

RideAnS [48]

Answer:

120 deet above ground level

Step-by-step explanation:

180 - 60 = 120

7 0

2 years ago

How do I do this problem?

Vikentia [17]

You use the distributive property and multiple everything inside of the parentheses by 2x^2 then everything in the parentheses by y to get 2x^4y-6x^3y^2+16x^2y^3. I think that’s the answer and I hope that helped!

8 0

3 years ago

If (a+b) = 4 and ab = 3, find the value of a³+b³.

Stolb23 [73]

Answer:

Step-by-step explanation:

a³+b³= (a+b)³ - 3ab(a+b)

= 4³ -3×3×4 = 64-36 = 28

8 0

2 years ago

Find one positive and one negative coterminal angle to 2.7 Radians:

Pavlova-9 [17]

the two coterminal angles to the given one are:

8.98 rad and -3.58 rad

<h3>How to find coterminal angles?</h3>

For a given angle A in radians, the family of coterminal angles is defined as:

B = A + n*(2*pi)

Where pi = 3.14 rad

Where n can be any integer number.

In this case, we have an angle of 2.7 radians, then the coterminal angles are:

B = 2.7 rad + n*(6.28 rad)

One positive is what we get if we select n = 1, then:

B = 2.7 rad + 1*(6.28 rad) = 8.98 rad.

And if we select n = -1, we get the negative coterminal angle:

B' = 2.7 rad - 1*(6.28 rad) = -3.58 rad

Then the two coterminal angles to the given one are:

8.98 rad and -3.58 rad

If you want to learn more about coterminal angles:

brainly.com/question/19891743

#SPJ1

4 0

2 years ago