All categories

3 years ago

Solve the logarithmic equation . Round the answer to four decimal places . 2^x =25

Mathematics

2 answers:

levacccp [35]3 years ago

8 0

Answer:

x = 4.6439

Step-by-step explanation:

2^x =25

Take the log of each side

log 2^x = log 25

We know that log a^b = b log a

x log 2 = log 25

Divide each side by log 2

x = log 25 / log 2

x =4.643856

Rounding to 4 decimal places

x = 4.6439

Korvikt [17]3 years ago

4 0

Answer:

x = 4.6439

Step-by-step explanation:

$2^{x} =25log 2^x = log 25\\log 2 = log 25x = log 25 / log 2\\x =4.643856\\x = 4.6439$

You might be interested in

What is the equation of the quadratic graph with a focus of (4,3) and a directrix of y=-6

Rufina [12.5K]

Answer:

f(x) = (1/18)x^2 - (4/9)x - 65/18

Step-by-step explanation:

Since the focus (4,3) is higher up than is the directrix y = -6, the vertex is between y = -6 and y = 3, halfway between these values, to be exact: y = -3/2. Thus, the y-coordinate of the vertex is (-6 + 3/2), or -4.5. The x-coordinate of the vertex is 4, which comes from that 4 in (4,3). Thus, the vertex is (4, -4.5) or (4, -4 1/2).

The standard equation for a vertical parabola with vertex at (h,k) is:

4p(y-k) = (x-h)^2, where p is the distance between vertex and focus or between vertex and directrix. In this case p = 4.5. Thus, the equation of this quadratic is 4(4.5)(y - [-4.5]) = (x - 4)^2, or

18(y+4.5) = (x-4)^2, or y+4.5 = (1/18)(x-4)^2.

Let's expand this and rewrite the result as a quadratic equation in standard form y = ax^2 + bx + c:

y + 4.5 = (1/18)(x^2 - 8x + 16). Multiplying all terms by 18 to remove both fractions, we get:

18y + 81 = x^2 - 8x + 16. Rearranging these terms, we get:

18y = x^2 - 8x + 16 - 81, or

18y = x^2 - 8x - 65, or

y = f(x) = (1/18)x^2 - (4/9)x - 65/18.

5 0

3 years ago

Read 2 more answers

The captain of a ship at point A and sailing toward point B observes a lighthouse at L and finds angle LAC to be 36*30'. After s

wel

Answer:

The distance between B and lighthouse is 3.8688 km

Step-by-step explanation:

Given:

The angle made from ship to lighthouse is 36.5 degrees

and that of point B is 73 degrees.

To Find:

Distance Between Point B and Lighthouse

Solution:

<em>Consider a triangle LAB(Refer the attachment )</em>

And Point C is on the line AB as A i.e. ship is sailing to B

So C is at 5 km from A.

Now In triangle LAC,

Using Trigonometry Functions as ,

tan(36.5)=LC/AC

LC=tan(36.5)*AC

=0.7399*5

=3.6998 km

Now In triangle LBC,

As,

Sin(73)=LC/LB

LB=LC/(Sin(73))

=3.6998/0.9563

=3.8688 km

LB=3.8688 km

6 0

3 years ago

What’s the answer? I’m very confused

Snowcat [4.5K]

F(x) = 29x +38. F(x) is a fancy way of saying y= and you must know the basic formula y=mx+b

6 0

4 years ago

A contractor records all of the bedroom areas, in square feet, of a five-bedroom house as: 100, 100, 120, 120, 180 What is the v

kifflom [539]

The variance is the total of the squared distances of the given data from the mean.

This can be calculated through the equation,

  σ² = summation of X² / N - μ²

where σ² is the variance X's are the data, N is the number of terms, and μ is the mean.

summation of X² = 100² + 100² + 120² + 120² + 180² = 81200
N = 5
  μ = (100 + 100 + 120 + 120 + 180) / 5
μ = 124

Substituting these values to the equation for variance,

  σ² = (81200/5) - 124² = 864

Thus, the variance is equal to 864.

4 0

3 years ago

Read 2 more answers

A bottle of perfume holds 0.55 onice. A bottle of cologne holds p.2 ounce. How many more ounces dose the bottle of perfume hold?

zimovet [89]

It has .33 more ounces if that says .2

7 0

3 years ago