Log Rules
Expand
log(7x)
log(7) + log(x)
Write the following equation as an exponential equation.
log x = 2
x=10^2
What is the rate r when the percent change is 34%?
r = 0.34
Solve for x
x=log_2 32
x=5
The constant variable discovered by Euler that is approximately equal to 2.718
e
Expand
log(7/x)
log(7) - log(x)
Write the following equation as an exponential equation.
ln 100 = x
e^x=100
Consider the exponential equation y=1000e^(0.35t) .
What is the starting amount modeled by the equation?
The starting amount is 1000
Write the exact value of x using logarithms
2^x=27
log_2 27
OR
log(27)/log(2)
The name of a logarithm that has a base of e
Natural logarithm
Condense into a single logarithm
5log(x)+log(y)-log(z)
log({x^5y}/z)
Write the following equation in logarithmic form.
(x+1)^2=14
log_(x+1) 14=2
Consider the exponential equation y=1000e^(0.35t) .
What is the rate modeled by the equation?
The rate is 0.35 or 35% (growth)
Find the two whole numbers that x in 2^x=27 is between
x is between 4 and 5
What base is a logarithm that doesn't have a subscript attached? For example, log 100
Base 10
Expand
log({7x^2}/y^3)
log(7)+2log(x)-3log(y)
Write the following equation in logarithmic form.
3^(x^2-1)=27
log_3(27)=x^2-1
If there are initially 3000 bacteria in a culture, and the number of bacteria increases continuously by 25% each hour, how many bacteria will there be in 5 hours? Round to the nearest whole number.
10,471 bacteria
Find the exact solution of x for 3^(7x)=2500
x={log_3 2500}/7
Logarithmic and Exponential functions have this type of relationship with each other
Inverse relationship
Condense into a single logarithm
6log(x)+4log(x)-7log(x)
logx^3
Write the following equation as an exponential equation.
log 30=x^2+2
10^(x^2+2)=30
If there are initially 3000 bacteria in a culture, and the number of bacteria increases continuously by 25% each hour, how long will it take for the bacteria to double? Round to the nearest whole number.
2.77 hours
Solve for the approximate solution of x: 3e^(3 - x)= 15
Round your answer to two decimal places.
x=1.39
What is it called when interest is NOT computed at specific periods of time? Instead, it is assumed to constantly be computed over time.
Continuously compounding interest