# Hotmath

Title:
Hotmath
Author:
Hotmath
Chapter: Exponential and Logarithmic Functions Section: Solving Exponential and Logarithmic Equations

Problem: 1

Solve log 5 40 = y and check the solution.

Problem: 3

Simplify.

log 14 36

Problem: 5

Evaluate the logarithm using the change of base formula.

log 6 320

Problem: 7

Check if x = e 9 is a solution of the equation:

ln x = 9

Problem: 9

Check if x = ln 2 is a solution of the equation:

4 e x = 8

Problem: 11

Solve the equation.

5 x = 625

Problem: 13

Solve for x .

8 e –x = 4

Problem: 15

Solve:

3 x = 10

Problem: 17

Solve for x .

7 x = 35

Problem: 19

Solve for x .

5 x – 6 = 4

Problem: 21

Solve for x :

Problem: 23

Solve for x .

4(2) 3 x – 3 = 12

Problem: 25

Solve the equation.

Problem: 27

Solve for x :

7 x = 3 x

Problem: 29

Solve:

10 x – 4 = 100 3 x – 7

Problem: 31

Solve for x :

2 5 x– 2 = 5 2 x+ 1

Problem: 33

Solve for x .

Problem: 35

Solve the equation. Check your solution.

Problem: 37

Solve the equation. Check your solution.

22 x + 2 = 57

Problem: 39

Solve the equation. Check your solution.

Problem: 41

Solve:

ln x = 5

Problem: 43

Solve 3 log 2 x = 15.

And check for extraneous solutions.

Problem: 45

Solve:

log 10 3 x = 1.5

Problem: 47

Solve the logarithmic equation.

3 log 2 x = –2

Problem: 49

Solve the logarithmic equation.

log x – log 4 = 4

Problem: 51

Solve the logarithmic equation.

2 log x – log 5 + log 3.2 = 12

Problem: 53

Solve ln (5 x + 1) = ln (3 x + 7).

And check for extraneous solutions.

Problem: 55

Solve ln x + ln ( x – 1) = 1, and check for extraneous solutions.

Problem: 57

Solve ln 6 (13 – 5 x ) = ln 6 (1 – x ).

And check for extraneous solutions.

Problem: 59

In order to double the investment in 5 years, at what rate of compound interest should the money be invested? Solve using common logarithms.

Problem: 61

Consider the following model, N = N 0 e 2 t , where N 0 is the initial number of particular species in a region and t is the time taken in years. How long will it take to triple in size?

Problem: 63

Lauren deposited \$ 800 in a bank that gives an annual interest of 6%. How long will it take for the deposit to reach \$1500, if compounded continuously?

Use the formula for continuous compounding : A = Pe rt