Quiz about Logs and Exponentials

Question 1

Which of the following is the graph of $$y = \log_2(x)$$ ?

Accepted Answer

A curve that passes through (1,0) and increases to the right.

Answer

A straight line passing through the origin.

Answer

A curve that passes through (0,1) and decreases to the right.

Answer

A parabola opening upwards.

Question 2

What is the inverse of the function $$y = \log_3(x)$$ ?

Accepted Answer

$$y = 3^x$$

Answer

$$y = \frac{1}{3^x}$$

Answer

$$y = \log_x(3)$$

Answer

$$y = x^3$$

Question 3

What is the formula for continuous compound interest?

Accepted Answer

$$A = Pe^{rt}$$

Answer

$$A = P(1 + \frac{r}{n})^{nt}$$

Answer

$$A = P(1 + rt)$$

Answer

$$A = P(1 - rt)$$

Question 4

Evaluate $$\log_{10}(1000)$$ .

Accepted Answer

$$3$$

Answer

$$1$$

Answer

$$2$$

Answer

$$4$$

Question 5

If $$y = e^x$$ , what is the value of $$x$$ when $$y = 1$$ ?

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$e$$

Answer

$$-1$$

Question 6

Condense the expression $$2\log_7(x) - \frac{1}{2}\log_7(y)$$ .

Accepted Answer

$$\log_7\left(\frac{x^2}{\sqrt{y}}\right)$$

Answer

$$\log_7\left(\frac{\sqrt{y}}{x^2}\right)$$

Answer

$$\log_7(x^2y^{1/2})$$

Answer

$$\log_7\left(\frac{x}{y}\right)$$

Question 7

Expand the expression $$\log_2(x^2y^3)$$ .

Accepted Answer

$$2\log_2(x) + 3\log_2(y)$$

Answer

$$\log_2(x^2) + \log_2(y^3)$$

Answer

$$2\log_2(x) - 3\log_2(y)$$

Answer

$$2\log_2(x) + \log_2(y^3)$$

Question 8

Which of the following is true for the graph of $$y = \log_b(x)$$ where $$b > 1$$ ?

Accepted Answer

It is an increasing function.

Answer

It is a decreasing function.

Answer

It is a constant function.

Answer

It is a quadratic function.

Question 9

Evaluate $$\log_5(1)$$ .

Accepted Answer

$$0$$

Answer

$$1$$

Answer

$$5$$

Answer

$$-1$$

Question 10

log₄(3x-1)=log₄(2x+3)

Accepted Answer

4

Answer

3

Answer

1

Answer

8

Question 11

log₈(4x+4)=2

Accepted Answer

15

Answer

12

Answer

10

Answer

3

Question 12

Solve the equation for x

Accepted Answer

1.771

Answer

0.5646

Answer

1.6203

Answer

1.8456

Question 13

Solve for x:
$$5^{4x-7}\ =5^{2x+3}$$

Accepted Answer

5

Answer

-5

Answer

2

Answer

3

Question 14

Solve for x using the same base method.
3^x-20= 27

Accepted Answer

23

Answer

17

Answer

27

Answer

-7

Question 15

Solve: 2^x = 4^x+1

Accepted Answer

-2

Answer

2

Answer

-3

Answer

3

Logs and Exponentials

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