Questions on Algebra: Exponent and logarithm as functions of power answered by real tutors!

Tutors Answer Your Questions about Exponential-and-logarithmic-functions (FREE)

Question 1205754: what is the inverse of y= 2e^(x-2)
Click here to see answer by greenestamps(13200)

Question 1206097: this year an estimated 4,325,000 people in this country are illiterate. With new incentives and funding, the country is hoping to cut that number by 3% every year. How many people do you predict will be illiterate in the year...
2035
2095
2155
Click here to see answer by math_tutor2020(3817)

Question 1206651: The population of J-Town in 2019 was estimated to be 76,500 people with an annual rate of increase of 2.4%.
Part A. Write an equation to model future growth.
Part B. What is the growth factor for J-Town?
Part C. Use the equation to estimate the population in 2072 to the nearest hundred people.

Click here to see answer by ikleyn(52800)

Question 1206832: The population of a colony of rabbits grows exponentially. The colony begins with 5 rabbits; 5 years later there are 320 rabbits.
(a) estimate how long it takes for the population of rabbits to reach 1000 rabbits.
Click here to see answer by josgarithmetic(39620)

Question 1206952: a^3 - b^2 = 11
a^2 + b = 13
Click here to see answer by MathLover1(20850)

Question 1206983: how long would it take for 1000 deposited in an account payinv 6% interest compounded countinously to earn 200 interest
Click here to see answer by ikleyn(52800)

Question 1207158: Log4x+log4(x-3)=1 find the solution
Click here to see answer by Edwin McCravy(20059)

Question 1207158: Log4x+log4(x-3)=1 find the solution
Click here to see answer by ikleyn(52800)

Question 1207302: The lengths of the sides of an equilateral triangle are log4(a), log10(b), log25(a+b) where A and B are positive numbers. What is the value of a/b?
Click here to see answer by greenestamps(13200)

Question 1207490: $5^{(}logx-1)/125=(1/5)^{(}logx)^{2}-logx$
Click here to see answer by ikleyn(52800)

Question 1207490: $5^{(}logx-1)/125=(1/5)^{(}logx)^{2}-logx$
Click here to see answer by Edwin McCravy(20059)

Question 1207550: Please help me solve the equation f(𝓍) = -log⅓ 3√𝓍 :
→ f(𝓍) = -log⅓ 3√𝓍
→ f(𝓍) = - ⅓ log⅓ 𝓍
→ f(𝓍) = ⅓ log3 𝓍

Click here to see answer by Edwin McCravy(20059)

Question 1208235: log[5](x-2)=3 logarithm to exponential form
Click here to see answer by mananth(16946)

Question 1208235: log[5](x-2)=3 logarithm to exponential form
Click here to see answer by math_tutor2020(3817)

Question 1208255: Hi, can you help with this question:
Use x=alphasintheta for sqrt(alpha^2-x^2), x= alphatantheta for sqrt(alpha^2+x^2) and x= alphasectheta for sqrt(x^2-alpha^2), to find int (x/(sqrt(1-x^2)^3) dx
Click here to see answer by Edwin McCravy(20059)

Question 1208258: Hi, can you help me with part b please:
A particle is oscillating in Simple Harmonic Motion and is 𝑥 metres away from the origin after 𝑡 seconds. The movement of the particle can be modelled with the equation 𝑥 = 2 cos(3𝑡 + 𝛼)
a) Prove that its acceleration is −9𝑥 𝑚𝑠^-2.
b) If initially, 𝑥 = 1𝑚 with velocity 3√3 𝑚𝑠^-1, find a suitable value for 𝛼.
Click here to see answer by ikleyn(52800)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by Edwin McCravy(20059)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by math_tutor2020(3817)

Question 1208301: Hi can you help please:
int (3 x^3) (sqrt(16-x^2)) dx
Just not sure if my trig substitutions are working
Click here to see answer by mccravyedwin(407)

Question 1208600: Bismuth-210 is an isotope that radioactively decays by about 13% each day, meaning 13% of the remaining Bismuth-210 transforms into another atom (polonium-210 in this case) each day. If you begin with 215 mg of Bismuth-210, how much remains after 7 days?
After 7 days, mg of Bismouth-210 remains.
Round your answer to the nearest hundredth as needed.

Click here to see answer by ikleyn(52800)

Question 1208757: Find the range of y = [[ 2x ]].

Note: [[ 2x ]] is a step function.
Click here to see answer by greenestamps(13200)

Question 1208756: Find the range of y = log[sqrt{e}].

Click here to see answer by greenestamps(13200)

Question 1208755: Find the range of y = e^x.

Click here to see answer by greenestamps(13200)

Question 1208812: Solve for x.

12^(sin x + cos x) + 24x^2 = 0
Click here to see answer by greenestamps(13200)

Question 1208811: Solve for x.
5^(sin x) - 5x + 10 = 0
Click here to see answer by ikleyn(52800)

Question 1208790: Solve for x.

5^(x + 2) + 6^x = 30
Click here to see answer by ikleyn(52800)

Question 1208832: Investing $8,000 for 6 years.
Option #1
7% compounded monthly
Option #2
6.85% compounded continuously
Which is the better investment?
Click here to see answer by math_tutor2020(3817)

Question 1208791: Solve for x.

12^(sqrt{x^2}) - 24^(x - 2) = 144
Click here to see answer by ikleyn(52800)

Question 1209240: A biologist is researching a newly discovered species of bacteria. At time T equals zero hours, he put 100 bacteria into what he has determined to be a favorable growth medium. Six hours later, he measures 450 bacteria. Assuming exponential growth, what is the growth constant K for the bacteria? (Round K2 decimal places) By what hour to the nearest 10 will there be 1000 bacteria?
Click here to see answer by timofer(105)

Question 1209241: Can you explain the quotient rule and the power rule and how to tell the difference between them in example. I’m confused how you know the difference and what they mean by the power rule.
Click here to see answer by Edwin McCravy(20059)

Question 1198664: An optical instrument with limiting magnitude L of any optical telescope and lens
diameter D, in inches, is given by
𝐿 = 8.8 + 5.1 𝑙𝑜𝑔 𝐷
a) Determine the limiting magnitude for a homemade I -inch reflecting telescope.
b) Determine the diameter of a lens that would have a limiting magnitude of R.

Click here to see answer by CPhill(1959)

Question 1209412: Find all real numbers x such that (3x - 27)^3 + (27x - 3)^3 = (3x + 27x - 30)^3.
Click here to see answer by Edwin McCravy(20059)

Question 1181507: Determine the absolute deviation and the coefficient of variation.
𝑦=[200.432 (±0.002)]^1/2 / log(20.42 × 10^15(±0.06))
Click here to see answer by CPhill(1959)

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