16 Answered Questions for the topic Natural Logs

Natural Logs Math Algebra 2 Logarithms


Solve the exponential equation. Express the solution as an exact answer in terms of natural logarithms

𝑒9−5𝑥=6981I got the decimal approximation of the answer but I have to enter the log version into webwork as well and because it is so specific about how the answer must be formatted I cannot seem... more
Natural Logs Differentiation


Differentiation- Urgent help needed

let 𝑈(𝑥, 𝑦) be defined for all x > 0, y > 0 by𝑈(𝑥, 𝑦) = ln(𝑥^a+y^a)-Ln(y^a) where 𝛼 is a positive constant find U'1(x,y), U'2(x,y) and U''12(x,y)
Natural Logs Precalculus


If lnm= 2.5 and lnw= 3, find a value for ln(m^6w^7)

Please show work
Natural Logs


Solve the equation for for x. e (to the power of e) to the power of x = 15

(ee )x = 15 

A pie cools in a 70 degree room. The pie is 300 degrees. After ten minuites the pie cools to 260 degrees

Create a formula then find the temp of the pie after 120 minuites 


implicitly differentiate y=e^(-mx)

I don't get how to do this and I'm not sure how to use the ln    y' = 


A sample of 400 g of radioactive lead-210 decays to polonium-210 according to the function A(t)=400e^-0.032t....

A sample of 400 g of radioactive lead-210 decays to polonium-210 according to the function A(t)=400e-0.032t,where t is time in years. Find the amount of radioactive lead remaining after (a) 4... more
Natural Logs


Use natural logarithms to solve the equation. 8e3x + 9 = 13.

I am really confused how to solve this, and how to put it into a calculator.   A)0.337 B)-2.838 C)0.058 D)-0.231

Natural Logarithms

e9-4x = 7472 We need to express the solution in terms of natural logarithms, having both the EXACT answer and the DECIMAL APPROXIMATION.Somehow got the decimal approximation, but not the exact... more
Natural Logs Calculus Derivative


Calculus + Natural Log + Derivative

Let f(x)= -5ln(6x)   I can't figure out how to find the fourth derivative.   f'(x)= -5/x   f'(4)= ___  


The value of the new car purchased for $27600 depricates 10%per year.

Write an exponential decay model for the value of the car.After about how many years will the car be worth half of its purchase price?
Natural Logs


Solve for x

ln(x+4) - ln18 = ln5
Natural Logs Equations Pre Calculus Logs


Natural Log Base Equation

7 e^x = -2 e^x + 5   Find x where e is the base of a natural log
Natural Logs


How do you prove log(a^x) = 1/log(x^a)

My teacher will give me extra credit if I can prove that   log(a^x) = 1/log(x^a)   Can you help? Thank you.
Natural Logs Calculus Limits


Limit of the following:

LIM x→1+       ((1/LN(x)) - (1/x2-1))
Natural Logs


3 lnx - 4lnx^4 = 2

Solve for x and give answers as exact solutions

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