Log help please

[Steph Annie]

Hi. I am drowning in a small pool of confusion here with logs. I am in "College Math 111.". Any help, explanations for the following problems would be really great! Thank you!

1. Write the following equation in logarithmic form and use your calculator to approximate your solution to the nearest thousandth.

10^x= 30

And this is what I did.

10^x = 30

ln[10^x] = ln (30)
x (ln)(10) =ln (30)
x= ln(30)/ln(10)
x approx. 1.4771

Is this right? Is there another way I could have solved it?


2. Write the following equation in exponential form and use your caclulator to approximate your solution to the nearest thousandth.

ln y = pi

b) e^2x+1 = pi

e^y =e^pi
y=e^pi

y approx to nearest thousandth = 23.141

Is this right? Is there another way I could have solved it?

3. What is the domain of the function g(x) = ln(3-x)

(3x-x) > 0
-x > -3
-x (-1) < -3 (-1)
x<3
Domain = ] - infinity; 3 [

Is this right? Is there another way I could have solved it?


4. Solve the following equations:

a) log₂ (x² - 2x) =3

Not sure. Help please!

5. The equation for continuously compounded interest is A = P * e^rt. At an interest rate of 4.5% how long will it take your original investment to triple in value? Round your answer to the nearest hundredth of a year.

Not sure....Help please!

 

[Deleted member 4993]

1. Write the following equation in logarithmic form and use your calculator to approximate your solution to the nearest thousandth.

10^x= 30

And this is what I did.

10^x = 30

When you are dealing with exponents of 10, it is generally "shorter" to work with Log₁₀.
10^x = 30

Log₁₀(10^x ) = Log₁₀(30)

x = 1.47712

2. Write the following equation in exponential form and use your caclulator to approximate your solution to the nearest thousandth.

ln y = pi

b) e^2x+1 = pi

e^y =e^pi
y=e^pi

y approx to nearest thousandth = 23.141

Is this right?

correct

4. Solve the following equations:

a) log₂ (x² - 2x) =3

Use definition of logs - i.e.

If Log_a(b) = c → a^c = b where a and b > 0.

5. The equation for continuously compounded interest is A = P * e^rt. At an interest rate of 4.5% how long will it take your original investment to triple in value? Round your answer to the nearest hundredth of a year.

A = P * e^rt

3*P = P * e^(0.045)t

Now solve for 't'.