Exponential & Logarithmic Review

Logs Converted to Exponential Functions

100

Write an exponential equation that is related with the given logarithmic equation:

log₃₆6=1/2

36^(1/2)=6

200

Write an exponential equation that is related with the given logarithmic equation:

log₉243=5/2

9^(5/2)=243

300

Write an exponential equation that is related with the given logarithmic equation: 

log₄(1/16) = -2

4^(-2)=1/16

400

Write an exponential equation that is related with the given logarithmic equation: 

log₅1/125=-3

5^(-3)=1/125

500

Write an exponential equation that is related with the given logarithmic equation:

log₁₀0.000001=-6

10^(-6)=0.000001

Properties of Logarithms

100

Rewrite each expression as a rational number or a single logarithm of the same base:

log_2(6)+log_2(8/3)

log₂(16)

= 4

200

Rewrite each of the following logarithmic expressions as multiple logarithms in expanded form.

log₃xy²

log_3(x)+2log_3(y)

300

Rewrite each of the following logarithmic expressions as multiple logarithms in expanded form.

ln(ab/c²)

ln(a)+ln(b)-2ln(c)

400

Using the inverse properties of the exponential and logarithmic expressions, simplify the expressions given.

e^ln(x+2)

x+2

500

Using the inverse properties of the exponential and logarithmic expressions, simplify the expressions given.

5^(2log_5(5x))

25x^2

Solving Logarithmic Equations

100

Solve for the following exponential equation. ROUND ANSWER TO THREE DECIMAL POINTS.

3e^2x+1=12

x=.193

200

Solve the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

log_2(x-3)=5

35

300

Solve the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

log(x-3)+log(x-4)=log(7-x)

5

400

Solve the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

15+log_2(2x)=20

16

500

Solve the logarithmic equation. ROUND ANSWER TO THREE DECIMAL POINTS IF NECESSARY.

-3+ln(2x-1)=-1

x=4.195

Solving Exponential Equations

100

2(3^(4x))=40

0.682

200

8e^(10x)=640

0.438

300

5(2^(3x))-4=46

1.107

400

1/2e^(x-4)=14

0.733

500

4/5(4^(2x-5))-4=20

3.727

INVERSE

100

Find the inverse of g(x)

g(x)=log(2x-3)-5

g^(-1)(x)=(10^(x+5)+3)/2

200

Find the inverse of f(x)

f(x)=2(3^(x+1))+10

f^(-1)(x)=log_3((x-10)/2)-1

300

Find the inverse of g(x)

g(x)=log(x-5)+8

g^(-1)(x)=10^(x-8)+5

400

Find the inverse of f(x)

f(x)=(5^(2x+10))-6

f^(-1)(x)=(log_5(x+6)-10)/2

500

Find the inverse of f(x)

f(x)=4log_2(x+3)-1

f^(-1)(x)=2^((x+1)/4)-3