Question 1

Solve for x.
-
A) 
B) 162
C) 
D) 1

Accepted Answer

The answer of Solve for x.
-
A) 
B) 162
C) 
D) 1...

Question 2

Express as a single logarithm.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express as a single logarithm.
-
A) 
B) 
C)...

Question 3

Solve.
-Given logb 4 = 1.079 and logb 12 = 1.934, evaluate logb 3.
A) 3.013
B) 0.855
C) 1.792
D) cannot be found using the properties of logarithms

Accepted Answer

Using the properties of logarithms, specifically the quotient rule which states that logb(x/y) = logb(x) - logb(y), we can find logb(3) by rearranging the given information. Since 12 can be expressed as 4*3, logb(12) = logb(4*3). Using the product rule, this can be rewritten as logb(4) + logb(3). We know logb(4) = 1.079 and logb(12) = 1.934. So, 1.934 = 1.079 + logb(3). Solving for logb(3), we get logb(3) = 1.934 - 1.079 = 0.855.

Question 4

Solve.
-Let logb A = 1.602 and logb B = 0.125. Find logb AB.
A) 12.816
B) 1.477
C) 0.200
D) 1.727

Accepted Answer

The property of logarithms that states logb(xy) = logb(x) + logb(y) is used here. So, logb(AB) = logb(A) + logb(B) = 1.602 + 0.125 = 1.727.

Question 5

Solve.
-Given logb 5 = 1.284 and logb 11 = 1.365, evaluate logb 6.
A) 16
B) cannot be found using the properties of logarithms
C) 55
D) 2.2

Accepted Answer

The given information does not provide a direct way to calculate logb 6 using the properties of logarithms, as there is no straightforward relationship between logb 5, logb 11, and logb 6.

Question 6

Using a calculator, find to the nearest ten-thousandth.
-ln 112
A) 0.2113
B) 2.0492
C) 41.3284
D) 4.7185

Accepted Answer

The answer of Using a calculator, find to the nearest...

Question 7

Solve for x.
-
A) 
B) 
C) 8
D) 1

Accepted Answer

The answer of Solve for x.
-
A) 
B) 
C) 8
D) 1...

Question 8

Solve.
-Let logb A = 2.572 and logb B = 0.262. Find logb  .
A) 2.834
B) 0.674
C) 2.310
D) 2.572

Accepted Answer

The answer of Solve.
-Let logb A = 2.572 and logb...

Question 9

Solve for x.
- = x
A) 1
B) 4477
C) 
D)

Accepted Answer

The answer of Solve for x.
- = x
A) 1
B) 4477
C)...

Question 10

Solve.
-Given  = 0.3010 and  = 0.4771, evaluate  72 .
A) 0.8616
B) 0.2549
C) 2.0333
D) 1.8572

Accepted Answer

The answer of Solve.
-Given  = 0.3010 and  =...

Question 11

Solve.
-Given  = 0.3010 and  = 0.4771, evaluate  .
A) 0.4308
B) 1.3801
C) 1.7323
D) 0.5044

Accepted Answer

The answer of Solve.
-Given  = 0.3010 and  =...

Question 12

Using a calculator, find to the nearest ten-thousandth.
-ln 0.995
A) 0.0050
B) -0.0022
C) 0.0022
D) -0.0050

Accepted Answer

The answer of Using a calculator, find to the nearest...

Question 13

Solve for x.
-
A) 
B) 8
C) 1
D) 8 ln e

Accepted Answer

The answer of Solve for x.
-
A) 
B) 8
C) 1
D) 8...

Question 14

Simplify.
-
A) 
B) 6 ln e
C) 6
D) 1

Accepted Answer

The answer of Simplify.
-
A) 
B) 6 ln e
C) 6
D) 1...

Question 15

Simplify.
-
A) 1
B) 3
C) a3
D)

Accepted Answer

The answer of Simplify.
-
A) 1
B) 3
C) a3
D) ...

Question 16

Express as a single logarithm.
-
A) 
B) 
C) 
D)

Accepted Answer

The answer of Express as a single logarithm.
-
A) 
B) 
C)...

Question 17

Solve for x.
-
A) 
B) 7
C) 
D) 1

Accepted Answer

The answer of Solve for x.
-
A) 
B) 7
C) 
D) 1...

Question 18

Solve.
-Given  = 0.3010 and  = 0.4771, evaluate 
A) 0.9030
B) 0.1436
C) 0.9542
D) 0.7781

Accepted Answer

The answer of Solve.
-Given  = 0.3010 and  =...

Question 19

Simplify.
-
A) a1948
B) 
C) 1
D) 1948

Accepted Answer

The answer of Simplify.
-
A) a1948
B) 
C) 1
D) 1948...

Question 20

Solve for x.
-
A) 9 ln e
B) 
C) 9
D) 1

Accepted Answer

The answer of Solve for x.
-
A) 9 ln e
B) 
C)...

Quiz 13: Exponential Functions and Logarithmic Functions

Solve for x. -

Express as a single logarithm. -

Solve. -Given logb 4 = 1.079 and logb 12 = 1.934, evaluate logb 3.

Solve. -Let logb A = 1.602 and logb B = 0.125. Find logb AB.

Solve. -Given logb 5 = 1.284 and logb 11 = 1.365, evaluate logb 6.

Using a calculator, find to the nearest ten-thousandth. -ln 112

Solve for x. -

Solve. -Let logb A = 2.572 and logb B = 0.262. Find logb .

Solve for x. - = x

Solve. -Given = 0.3010 and = 0.4771, evaluate 72 .

Solve. -Given = 0.3010 and = 0.4771, evaluate .

Using a calculator, find to the nearest ten-thousandth. -ln 0.995

Solve for x. -

Simplify. -

Simplify. -

Express as a single logarithm. -

Solve for x. -

Solve. -Given = 0.3010 and = 0.4771, evaluate

Simplify. -

Solve for x. -