Properties of logarithms assignment

Which is equivalent to 3log28 + 4log212 − log32?

5-log3(2)

Write the following expression as a single logarithm with coefficient 1. log910 − log9 12 − log94

log 9(5)

Expand: log20 mn5p

log20m-5log20n-log20p

Complete the steps to evaluate the following expression, given log3a = −0.631. log3 a3

log3(3)=1 log3(a/3)=-1.631

Write the following expression as a single logarithm with coefficient 1. log3(6c) + log3112

log3(c/2)

Rewrite the following expression as a single logarithm with coefficient 1. 3log5 uv2w3

log5(u^3v^6/w^9)

Complete the steps to evaluate log798, given log72 ≈ 0.356. How can you rewrite log798 using the product property?

log7(2)+log7(49) log7(49)=2 log7(98)=2.356

The proof for the product property of logarithms requires simplifying the expression logb(bx+y) to x + y. Which property is used to justify this step?

logb(b^c)=c

Use the properties of logarithms to write the following expression as one logarithm. logslogr + 8logr s − 3logr t

logr(s9/t3)

Evaluate log12y2, given log12y = 16.

32

Choose the letter of the expression listed on the right that completes each step to show how to use the power and product properties of logarithms to prove that the quotient property is true for logbxy. logb xy

C A D B

Benford's law states that the probability that a number in a set has a given leading digit, d, isP(d) = log(d + 1) - log(d).State which property you would use to rewrite the expression as a single logarithm, and rewrite the logarithm. What is the probability that the number 1 is the leading digit? Explain.

Use the quotient property to rewrite the expression. Write the difference of logs as the quotient log((d+1)/d). Substitute 1 for d to get log(2). Since log(2) = 0.30, the probability that the number 1 is the leading digit is about 30%.