Exponentials and Logarithms

Rewrite in exponential form:
ln(2) = x

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

Tags

CCSS.HSF.BF.B.5

Convert 6^(x+2)=216 to logarithmic form

• log₂₁₆(x+2)=6
• log₆(x+2)=216
• log₆(216)=x+2
• log_(x+2)(216)=6

Tags

CCSS.HSF.BF.B.5

Convert log₈(x+2)=3 to exponential form.

• 8^(x+2)=3
• 3^(x+2)=8
• 8³=x+2
• 3⁸=x+2

Tags

CCSS.HSF.BF.B.5

 $A\left(t\right)=P\left(1+\frac{r}{n}\right)^{n\cdot t}$  

Find the time required for an investment of $1000 to grow to $5000 at an interest rate of 8% per year compounded monthly. (round to nearest year)
Use

• 1 year

• 242 years

• 20 years

• 13 years

A household appliance loses its value after it is purchased. Its current value, V(t), can be modeled by the function, V(t)= V₀(3/4)^t, where V₀ is the original price, and t is the number of years. How long will it take for a refrigerator initial cost $850 to be worth $65? Round to the nearest year.

• 9 years

• 13 years

• 8 years

• 10 years

Solve the equation.  Check for extraneous solutions.

 $-2\ln\left(2w-3\right)=-10$  

•  $w=75.707$  

•  $w=42.852$  

•  $w=68.724$  

•  $w=13.905$  

Solve the equation.

 $\left(\frac{1}{9}\right)^k\cdot27^{\left(k+4\right)}=\left(\frac{1}{81}\right)^{\left(3-k\right)}$  

•  $k=8$  

•  $k=12$  

•  $k=6$  

•  $k=4$  

A wildlife organization released a group of endangered animals into a preserve. Their population after t months can be modeled by the function below. What will the population be after 16 months.

 $P=\frac{1500}{1+8e^{-0.15t}}$  

• 869

• 468

• 1242

• 948

Patrick invested $1500 into an account with an interest rate of 6.5%. How much will be in the account if the interest is compounded monthly for 20 years?

Use the compound interest formula.

• $5,484.67

• $472,409,182.30

• $12,415.42

• $112,482.92

Write the equation in logarithmic form.
 $e^{\left(x-9\right)}=74$  

•  $\ln\left(x-9\right)=74$  

•  $x-9=\ln74$  

Tags

CCSS.HSF.BF.B.5