$MathMaster logo$

MathMaster

Home
general
solve the following equation for x in exact form and then find the value to the nearest hundredths make sure to show your

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

$Expert avatar$

4.5

112 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)

Question: Find the integral of the function f(x)=3x^2+2x-1 from x=1 to x=4.

+

What is the equation for the Pythagorean Theorem in a right triangle?

+

What is the number of ways to arrange the letters in the word "COMBINATORICS"?

+

New questions in Mathematics

Add. 7/w²+18w+81 + 1/w²-81

Consider numbers from 1 to 2023. We want to delete 3 consecutive, so that the avarage of the left numbers is a whole number. How do we do that

The actual length of an object is 1.3 m . If the blueprint uses a scale of 1 : 12 , what is the length of the line on the drawing?

The mean life of a television set is 119 months with a standard deviation of 13 months. If a sample of 67 televisions is randomly selected, what is the probability that the sample mean would be less than 121 months? Round your answer to four decimal places

A person borrows rm 1000 from a bank at an interest rate of 10%. After some time, he pays the bank rm 1900 as full and final settlement of the loan. Estimate the duration of his loan.

find all matrices that commute with the matrix A=[0 1]

show step by step simplification: (¬𝑑∨((¬b∧c)∨(b∧¬c)))∧((𝑎 ∧ 𝑏) ∨ (¬𝑎 ∧ ¬𝑏))∧(¬𝑐∨((¬𝑑∧𝑎)∨(𝑑∧¬𝑎)))

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

There are 3 orchards, a, b and c. Orchard a has 60 fewer trees than orchard b orchard c has 3 times as many trees as orchard b. If the three orchards have 430 trees altogether, how many trees does orchard c have?

Use linear approximation to estimate the value of the sine of 31o.

If a|-7 and a|9, then a|-63

A cell phone company offers two calling plans. Plan A: $20 per month plus 5 cents for each minute, or Plan B: $30 per month plus 3 cents for each minute. [2] Write an equation to describe the monthly cost (a) C (in $) in terms of the time m (in minutes) of phone calls when Plan A is applied.

Calculate the difference between 407 and 27

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.

-Please answer to the following questions: What is the price elasticity of demand? Can you explain it in your own words? What is the price elasticity of supply? Can you explain it in your own words? What is the relationship between price elasticity and position on the demand curve? For example, as you move up the demand curve to higher prices and lower quantities, what happens to the measured elasticity? How would you explain that? B-Assume that the supply of low-skilled workers is fairly elastic, but the employers’ demand for such workers is fairly inelastic. If the policy goal is to expand employment for low-skilled workers, is it better to focus on policy tools to shift the supply of unskilled labor or on tools to shift the demand for unskilled labor? What if the policy goal is to raise wages for this group? Explain your answers with supply and demand diagrams. Make sure to properly cite and reference your academic or peer-reviewed sources (minimum 2).

(3b)⋅(5b^2)⋅(6b^3)