Properties of Logarithms Equations

• True, subtraction between two logarithms converts to division of those two logarithms in condensed form.

• True, a logarithm is an exponent. When dividing like bases you subtract exponents, therefore dividing logarithms as in this example.

• False, subtraction between two logarithms is division within a single logarithm in condensed form.

• False, it is not possible to condense the expression.

log(x+6) = 1

• 4

• 4.222

• -5

• -9.550

log₂32=3x

• 5/3

• 3/5

• 5

• 3

• 4

log_x1000=3

• 1

• 10

• 30

• 3

Expand.

• log x + log y + log z

• log x + log y + log z

• log x - log y - log z

• log x + log y + log z

Expand:

log₃(9x²)

• 3 + 2log₃(x)

• log₃(81) + 2log₃(x)

• 2 + 2log₃(x)

• log(9) + 2log(x)

log (x) + log (x) = log (25)

• -5, 5

• 5

• -5

• 25

• No solution (extraneous solutions)

Solve for x

• x = 5

• x = -5

• x = 5, -5

• No solution, only extraneous solutions

Solve the equation. Select all solutions. Check for extraneous solutions.

• -2

• 5

• 2

• -5

• 0