Review of exponential function and logarithmic function

Exponential function

100

What is the domain of the exponential function y=a^x

all real numbers

200

What is the range of the exponential function y=a^x

y>0

300

Use the graph of f to describe the transformation that yields the graph of g.

f(x)=3^x, g(x)=3^x+1

shift one unit up

400

Use the graph of f to describe the transformation that yields the graph of g.

f(x)=10^x, g(x)=10^-x

reflect over y-axis

500

Use the graph of f to describe the transformation that yields the graph of g.

f(x)=0.3^x, g(x)=-0.3^x+5

reflect over x-axis and shift 5 units up

logarithmic function

100

What is the domain of the logarithmic function y=log_a^x?

x>0

200

What is the range of the logarithmic function y=log_a^x?

all real numbers

300

Find the value of log₂⁸=

3

400

Find the value of log¹⁰⁰=

2

500

Use the graph of f to describe the transformation that yields the graph of g.

f(x)=log₂^x, g(x)=log₂^x-2+3

shift two units to the right and shift 3 units up

convert between Exponential and logarithmic function

100

Write the exponential equation in logarithmic form.

5³=125

log₅¹²⁵=3

200

Write the logarithmic equation in exponential form.

log^1/10=-1

10^-1=1/10

300

Write the exponential equation in logarithmic form.

24⁰=1

log₂₄¹=0

400

Write the logarithmic equation in exponential form.

log₃₂⁴=2/5

32^2/5=4

500

Use the properties of logarithms to simplify the expression.

9^log₉¹⁵=

15

solve exponential equation

100

Use the one-to-one property to solve the equation for x.

3^x+1=27

x=2

200

Use the one-to-one property to solve the equation for x.

(1/2)^x=32

x=-5

300

Use the one-to-one property to solve the equation for x.

5^x-2=1/125

x=-1

400

Use the one-to-one property to solve the equation for x.

e^3x+2=e³

x=1/3

500

Use the one-to-one property to solve the equation for x.

e^{x^2+6}=e^5x

x=2, x=3

solve logarithmic function

100

Use the one-to-one property to solve the equation for x.

log₅^(x+1)=log₅⁶

x=5

200

Use the one-to-one property to solve the equation for x.

log(5x+3)=log12

x=9/5

300

Find the domain, x-intercept, and vertical asymptote of the logarithmic function.

f(x)=log₄^x

domain: x>0

x-intercept:(1,0)

vertical asymptote: x=0

400

Find the domain, x-intercept, and vertical asymptote of the logarithmic function.

f(x)=log₄^(x-3)

domain: x>3

x-intercept: (4,0)

vertical asymptote:x=3

500

Find the domain, x-intercept, and vertical asymptote of the logarithmic function.

y=log₅^(x-1)+4

domain: x>1

x-intercept: x=626/625

vertical asymptote: x=1