9.1 Homework Problems: Introduction to Logarithms

1. Write each equation in log form

a. 7² = 49

b. 4^k = 11.6

c. 10³ = 1000

d. [latex]\left(\frac{3}{4}\right)^4=\ \frac{81}{256}[/latex]

e. 10^k = x

2. Express each log as an exponent

a. log₃ (9) = 2

b. log_b (39) = 10

c. log_b (4) = [latex]\frac{2}{3}[/latex]

d. log_n (y²) = x

e. log (1000) = 3

f. log (10) = 1

3. Evaluate the following and round to the nearest ten-thousandths

a. log (176)

b. log (0.0061)

4. Solve for x (round each answer to the nearest hundredth)

a. log₄ (x) = 2

b. log₅ [latex]\frac{1}{125}[/latex] = x

c. log_x (32) = 5

d. log₅ ([latex]5^{\log_5(25)}[/latex] = x

e. log x = -1.7

f. 5 log x = 9.4

g. 2^x+3 = 6

h. 4^x = 24

i. 9 + 3^x = 31

j. 5^3x = 18 ^{(x – 2)}

k. 12^8x = 13 ^{(x + 5)}

Use the change of base formula to find exact answers (round to the nearest hundredth)

a. log₃ (346)

b. log₅ (200)

c. 2 log₆ (33)

d. 4 log₅ (413)

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