Solving Log Equations

Question 1

Product Law

Answer 1

Logb = log[b]m + log[b]n

When adding logs of same base multiply, or when multiplying add.

Question 2

Quotient Law

Answer 2

logb = log[b]m - log[b]n

When subtracting logs of same base divide, when dividing subtract

Question 3

Simplify? Evaluate? Evaluate exactly?

Answer 3

Simplify: write in simplest form. Ex. log14. Evaluate: solve even to fractions or decimals. Evaluate exactly: only whole numbers or fractions

Question 4

Techniques for solving exp equation

Answer 4

If the equation can be written w/a common base do it! If it cant easily, use logs. If more complicated, creatively choose an effective mathematical solution

Question 5

Prove Quotient Law

Answer 5

Let log[b]m = x and log[b]n = y
m / n = b^x / b^y
m / n = b^(x-y)

Question 6

How to solve exponential equations with completely different bases?

Answer 6

write as base of one number. Ex. 3^x = 2^x+2 can be (2^log3/log2)^x = 2^x+2. OR take log of both sides.