Question

Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25

258

likes
1288 views

Answer to a math question Solve the following equation for x in exact form and then find the value to the nearest hundredths (make sure to show your work): 5e3x – 3 = 25

Expert avatar
Santino
4.5
111 Answers
To solve the equation 5e^(3x) - 3 = 25 for x, we first add 3 to both sides of the equation to get: 5e^(3x) = 28 Next, we divide both sides by 5 to isolate e^(3x): e^(3x) = 28/5 To solve for x, we take the natural logarithm of both sides of the equation: ln(e^(3x)) = ln(28/5) Using the property of logarithms that ln(e^a) = a, we can simplify the left side of the equation: 3x = ln(28/5) Finally, we divide both sides by 3 to solve for x: x = (1/3)ln(28/5) Using a calculator, we can evaluate this expression to two decimal places: x ≈ 0.77 Therefore, the solution to the equation 5e^(3x) - 3 = 25 is x ≈ 0.77

Frequently asked questions (FAQs)
What is the product of 10 and the sum of 5, 8, and 12?
+
Find the smallest positive angle in degrees for which the cosine value is equal to 0.5.
+
Can you prove that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent?
+
New questions in Mathematics
Simplify the expression sin³(x)+cos³(x), using trigonometric functions
-6(3x-4)=-6
Determine the absolute extrema of the function 𝑓(𝑥)=𝑥3−18𝑥2 96𝑥 , on the interval [1,10]
Suppose X has a Poisson distribution, with a mean of 0.4. Determine the probability that x is at most 2.
-3x 2y = -6; -5x 10y = 30
Pedro had 80% of the amount needed to buy a game. Of this amount, you spent 15% on a watch and therefore, you will need to add another R$640.00 to purchase this game. Is the value of the game?
Find 2 numbers whose sum is 47 and whose subtraction is 13
3.24 ÷ 82
30y - y . y = 144
Fill in the P(X-x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -5 ,3 , 4, 5 , and 6.
List five numbers that belong to the 5 (mod 6) numbers. Alternate phrasing, list five numbers that satisfy equation x = 5 (mod 6)
Take the limit of (sin(x-4))/(tan(x^2 - 16) as x approaches 4.
(X+2)(x+3)=4x+18
there are 500,000 bacteria at the end of a pin point. 1000 bacteria can make a person sick. then bacteria at the tip of a pin point can make 500 people sick. Also, many people do not know that bacteria can (reproduce). Let's say there are 5 bacteria and we leave it for 15 minutes. bacteria will multiply to 10. if left for up to 30 minutes, 20 bacteria will form. if left up to 45 minutes. bacteria will multiply up to 40. every 15 minutes the bacteria will double 2. if you start with five bacteria that reproduce every 15 minutes, how manu bacteria would you have after 12 hours ?
22. Let [AB] be a chord in a circle C, and k a circle which is internally tangent to the circle C at a point P and to the chord [AB] at a point Q. Show that the line P Q passes through the midpoint of the arc AB opposite to the arc APB.
a coffee shop has 9 types of creamer and 11 types of sweetener. In how any ways can a person make their coffee?
Emile organizes a community dance to raise funds. In addition to paying $300 to rent the room, she must rent chairs at $2 each. The quantity of chairs rented will be equal to the number of tickets sold. She sells tickets for $7 each. How much should she sell to raise money?
answer this math question The scale on a map is drawn so that 5.5 inches corresponds to an actual distance of 225 miles. If two cities are 12.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) miles apart. The two cities are how many miles apart
The company produces a product with a variable cost of $90 per unit. With fixed costs of $150,000 and a selling price of $1,200 per item, how many units must be sold to achieve a profit of $400,000?
An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?