Exponential and Logarithmic Equations
Find the solution of the exponential equation
e^(1-2x)=e^(4x-7)
What is
4/3?
The parent graph of logarithmic functions
What is
y=log_b(x)?
Use the Laws of Logarithms to expand the expression
log(ab^2)
What is
loga+2logb?
Write in exponential form: log_4(1/16)=-2
What is
4^-2=1/16?
If $5400 is invested at an interest rate of 3.5% per year, compounded continuously, find the value of the investment after 2 years.
What is $5791.54?
The value of x in the equation.
log4x-log15=4
What is 37500?
This type of asymptote appears in logarithmic functions because of their limited domain.
What is a vertical asymptote?
This expression simplified
((2x)/(3sqrty))^-4
What is
(81y^2)/(16x^4)?
Rewrite as a power of x:
root(3)(x^2)
What is
x^(2/3)?
If $750 is invested at an interest rate of 3.75% per year, compounded quarterly, find the value of the investment after 5 years.
What is $903.88?
The value of x in the equation
2(5+3^(x+1))=100
What is
log_3(45)-1?
or about
2.465
Find the domain of the following function
f(x)=log_5(x-7))
What is
x>7?
The following expression simplified
(24e^x*e^3)/e^-5
What is
24e^(x+8)?
Write in logarithmic form: e^(2x)=10x-3
What is
ln(10x-3)=2x?
If $925 is invested at an interest rate of 2.5% per year, find the amount of the investment at the end of 10 years, given that it is being compounded semiannually.
What is $1185.88?
Solve for x
ln(x-1/2)+ln2=2lnx
What is
x=1?
The domain of the function
f(x)=-2ln(8-2x)
What is
x<4?
Use laws of logarithms to evaluate the expression
log_3(100) - log_3(18) - log_3(50)
What is -2?
Rewrite in exponential form: log(5x^2)=3
What is
10^3=5x-2?
After earning interest for 5 years, an account has a balance of $100000. Assuming interest is compounded monthly, what was the initial value of the account 5 years ago?
What is $67,121.04?
Solve the equation
x^2 * 2^x - 2^x = 0
What is
+-1?
The domain of the function
f(x)=ln(4-x^2)
What is
-2<x<2?
This expression written as a single logarithm
3ln2+2lnx-(1/2)ln(x+4)
What is
ln((8x^2)/sqrt(x+4))?
Rewrite in exponential form: 2lnx=25x+7
What is
e^(25x+7)=x^2?
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t)=13e^(-0.015t) , where m(t) is measured in kilograms.
How much of the mass remains after 45 days?
What is 6.62 kg?