Exponential and Logarithmic Functions

Solving

100

If y = 3 • 4^x, what is the value of y when x = 5?

3072

200

If 2048 = 4 • b³, what is the value of b?

8

300

If y = 5 • e^0.05x, what is the value of y when x = 11?

57.820

400

If y = 6 • 2^x, what is the value of x when y = 40?

2.737

500

If y = 6 • e^2x, what is the value of x when y = 20?

1.407

Evaluating

100

Find the value of 1.05¹³.

1.886

200

Find the value of ln(432).

6.068

300

Find the value of log_51.234(1).

0

400

Find the value of 3 log(1000).

9

500

Find the value of log₃(8700).

8.257

Rewriting

100

Rewrite the equation 25=log₂x as an exponential function.

2²⁵=x

200

Rewrite the equation 9^z=k as a logarithmic function.

z = log₉(k)

300

Rewrite (2x)^¾ as a radical expression.

⁴√(2x)³

400

Rewrite 5 = e^h as a logarithmic expression.

ln(5) = h

500

Rewrite 650 = 10^x as a logarithmic expression

log(650) = x

Keep It Simple

100

Simplify the expression 4m^-4 • 2m^-3.

8 / m⁷

200

Simplify the expression 2x³y² • 4xy.

8x⁴y³

300

Simplify the expression 2v² • (v³)^-3

2 / v⁷

400

Simplify the expression (x³)⁴ • x^-3y⁴.

x⁹y⁴​​​​

500

Simplify the expression (16x⁴)^½ • 2x^-2

8

Words, Words, Words

100

My apartment is rent controlled, which means rent only goes up by 2% a year. If I currently pay $2800 a month, how much will my rent be in 5 years? 

$3091.43

200

My YouTube channel had 25 subscribers. In 5 months, I reached 100 subscribers through exponential growth – as a percentage, what is my monthly increase in subscribers?

31.951%

300

A town's population is currently 5400. If the population grows continuously at 4% a year, what will the population be in 6 years?

6864

400

I currently have $50,000 in an investment account that gives me 4% annual returns. How long until my account reaches $1 million?

76.381 years

500

A tech CEO has $500,000 invested in company stocks, which grows at a continuous rate of 4% a year. How long until this investment reaches $1 million?

17.329 years