Exponential and Logarithmic Forms
Identify the base in the following expression.
2^3=8.
What is "2"?
True or False. The quotient property allows a logarithm that contains a quotient to be rewritten as two logarithms with a subtraction where the term that is in the denominator is the argument of the first logarithm in the subtraction.
What is "False"?
Solve the following equation.
x^(3/4)=8
What is "16"?
What are the two most common bases for logarithms?
What is "10 and e"?
Solve the following equation.
log(base 4) 64=x
What is "x=3"?
Convert the following to exponential form.
log (base 3)81=4
What is "3^4=81"?
When rewriting an argument of a logarithm that is written as a radical, you can rewrite the argument with a rational exponent. The index of the radical becomes which part of the rational exponent?
What is "the denominator"?
7^n=343
What is "3"?
True or False. When setting up a change of base problem, the base of the original logarithm becomes the numerator of the quotient.
What is "False"?
Solve the following equation.
2logx=2
What is "x=10"?
Convert the following to logarithmic form.
6^2=36
What is "log (base 6) 36=2"?
Expand the following logarithm.
log (3pt)
What is "log 3 + log p + log t"?
Solve the following equation.
3+9^2x=30
What is "3/4"?
Set up the following using the Change of Base Theorem.
log (base 4) 32.
What is " log 32/ log 4"?
Solve the following equation. Express your answer as a fraction, if necessary.
log (2x+5)=3
What is "995/2"?
Evaluate the following logarithmic expression.
log (base 5) 1/125
What is "-3"?
Condense the following logarithm.
4logy-5logn
What is "log(y^4)/(n^5)"?
Solve the following equation. Round to the nearest hundredth.
8^x=58
What is "1.95"?
Evaluate the following logarithm. Round to the nearest thousandth.
log (base 2) 15.
What is "3.907"?
Solve the following equation. Express your answer as a fraction, if necessary.
log (3x+2) - log (x-1)=1.
What is "x= 12/7"?
Evaluate the following logarithmic expression.
log 10,000
What is "4"?
Expand the following logarithm.
log (5x/4y)
What is "log 5 + log x - log 4 - log y"?
Solve the following equation. Round to the nearest hundredth.
8^(n+1)=3.
What is "-0.47"?
Evaluate the following logarithm. Round to the nearest hundredth.
log (base 6) 10.
What is "1.29"?
Solve the following equation. Express your answer as a fraction, if necessary.
log (x+21) + logx =2
What is "x=4"?