Applications of Logarithms

Given log₂ b = x and log₂ c = y, express log₄ (8b/c ) in terms of x and y.

Which equation is equivalent to: log₂ 18 = x - 1

• 2¹⁸ = x - 1

• 2^{(x - 1)} = 18

• 18² = x - 1

• 18^{(x - 1)} = 2

• 2,3220

• 2.3218

• 2.3219

• 2.322

You invest $15,000 with an interest rate of 8% per year compounded continuously. The function A\left(t\right)=15000e^{0.08t} models the situation. What set up will allow you solve for how long it will take for the investment to grow to $45,000 ?

• 45000=15000e^{0.08t}

• A\left(3\right)=15000e^{0.08\left(3\right)}

• A\left(45000\right)=15000e^{0.08\left(45000\right)}

• 3=15000e^{0.08t}

What would the next step in solving 3=e^{0.08t} be ?

• Divide both sides by 3

• Divide both sides by e

• Take the natural log of both sides

• Rewrite the exponent 0.08t as the coefficient of "e"

• Subtract e to both sides

Condense

• logxyz³

• log(xy/z³)

• logx+logy+logz³

• logx³y³z³

Condense

• log₈(a¹⁸/b³)

• log₈(a¹⁸b³)

• log₈(a/b³)

• 15log₈(a/b³)

Expand

• A

• B

• C

• D

Use the properties of logarithms to retwrite

• A

• B

• C

• D