Log & Exponential Functions Test

Which graph below matches the function: f(x) = (1/3)^x

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A car depreciates at a rate of 12% per year. How long will it take for a $30,000 vehicle to be worth $20,000?

• -3.17 years

• 3.58 years

• 3.17 years

• 4.12 years

Evaluate log₃27

• 3
• 9
• 27
• -3

Rewrite 3⁴ = 81 in logarithmic form.

• log₃4 = 81
• log₈₁3 = 4
• log₃81 = 4
• log₄81 = 3

Tags

CCSS.HSF.BF.B.5

Rewrite log_pt = m in exponential form.

• p^t = m
• t^m = p
• m^t = p
• p^m = t

Tags

CCSS.HSF.BF.B.5

Use multiple log properties to write as a single log:

3log₂x - log₂y + log₂z

• $\log_2\ \frac{x}{yz}$

• $\log_2\ \frac{x^3}{yz}$

• $\log_2\ \frac{x^3z}{y}$

• $\log_2\ \frac{xz}{y}$

Rewrite in exponential form:
ln(2) = x

• 2^x = 10
• 10² = x
• e^x = 2
• e² = x

Expand

• 4log₄u - 16log₄v

• 4logu + 16logv

• 4logu - 4logv

• 4logu - 16logv

Solve: 9^8-x = 27^x-3

• 5
• -5
• 1/5
• -1/5

Solve log₂(x + 5) = 3

• 3

• 4

• 5

• 6