Re-writing Logs
Write the following as a single logarithm:
log_3x+log_3y
log_3xy
Rewrite the following as an exponential equation
log_3(9)=2
3^2=9
Solve for x
log_7x=2
x=49
Find the pH of a substance if the hydrogen ion concentration [H+] is 5.6 * 10^-11. Round to the nearest hundredth
pH=-log[H^+]
10.25
Which property was used to condense the following logarithmic expression?
log_3 4 +log_3y
Product property only
Rewrite the following logarithmic expression as a single log.
3n6-3ln7
ln(6/7)^3
Rewrite the following exponential equation as a logarithmic equation.
3^x=27
log_3 27=x
Solve the following equation
log_0(-2/3)=x
No solution
A bank account balance can be calculated using the equation below. Find the amount of money in the account after 3.5 years.
A=1100(1.011)^(12t)
A=$1741.57
Which property was used to expand the following logarithmic expression?
log_3 (x/y)=log_3x-log_3y
Quotient property only
Rewrite the following logarithmic expression as a single log.
3log_2 x-3log_2 y
log_2 (x/y)^3
Rewrite the following in exponential form. Do NOT solve for x.
log_6(2x)+1=3
6^2=2x
OR
2x=6^2
Solve the following equation.
log(2x+36)=2
x=32
Find the concentration of hydrogen ions in a solution if the pH is 5.3.
pH=-log(H^+)
5.0*10^-6
Which property or properties would be used expand the following logarithmic expression?
log_3(m^2/n)
Power & quotient properties
Fully expand the following logarithmic expression.
log_5 3x^4
log_5 3+4log_5x
Re-write the following in logarithmic form. Do NOT solve for x.
7^(2x-6)=52
2x-6=log_7 52
Solve the following equation for x.
2log(x)=log(49)
x=7
A certain chemical has a half-life of 3 hours. Calculate the number of hours it would take for 500 milligrams of the chemical to decay to 15.625 milligrams.
15 hours
Which logarithmic property was used incorrectly?
3logs+2logt-logu
log((st^2)/u)^3
Power property
Rewrite the following as a single logarithmic expression
5log_3x+3log_3y-2log_3z
log_3((x^5y^3)/z^2)
Re-write the following in logarithmic form. Do NOT solve for x.
5^(3x-2)+2=13
log_5 11=3x-2
DAILY DOUBLE!!
Solve the following for x.
logx+log(x+2)=log(15)
x=3
A bank account balance can be calculated using the equation below. Find the time it would take for the balance to exceed $1,750. Round to the nearest year.
A=600(1.015)^(12t)
6 years
Which properties were used to rewrite the following logarithmic expression?
3log_2a+log_2b-3log_2c=log_2((a^2b)/c^3)
Product property, Quotient property, & Power property