Technical Mathematics, Sixth Edition

18.6. CHAPTER 18 REVIEW PROBLEMS

Convert to logarithmic form.

1. x^5.2 = 352 log_x352 = 5.2

2. 4.8^x = 58 log_4.8 58 = x

3. 24^1.4 = x log₂₄ x = 1.4

Convert to exponential form.

1. log₃ 56 = x 3^x = 56

2. log_x 5.2 = 124 x¹²⁴ = 5.2

3. log₂ x = 48.2 2^48.2 = x

Solve for x.

1. log₈₁ 27 = x 3/4

2. log₃ x = 4 81

3. 

Write as the sum or difference of two or more logarithms.

Express as a single logarithm.

1. log 5 + log 2 log 10

2. 2 log x − 3 log y log(x²/y³)

3. 

Find the common logarithm of each number to four decimal places.

1. 6.83 0.8344

2. 364 2.5611

3. 0.00638 −2.1952

4. 18.6 1.2695

5. 87.4 1.9415

Find x if log x is equal to the given value.

1. 2.846 701.5

2. 1.884 76.56

3. −0.473 0.337

4. 3.361 2296

Find the natural logarithm of each number to four decimal places.

1. 84.72 4.4394

2. 2846 7.9537

3. 0.00873 −4.7410

Find the number whose natural logarithm is the given value.

1. 5.273 195.0

2. 1.473 4.362

3. −4.837 7.931 × 10⁻³

Find log x if

1. ln x = 4.837 2.101

2. ln x = 8.352 3.627

Find ln x if

1. log x = 5.837 13.44

2. log x = 7.264 16.73

Solve for x to three significant digits.

1. (4.88)^x = 152 3.17

2. e^2x+1 = 72.4 1.64

3. 3 log x − 3 = 2 log x² 1.00 × 10⁻³

4. log(3x − 6) = 3 335

5. A sum of $1500 is deposited at a compound interest rate of compounded quarterly. How much to the nearest dollar will it accumulate to in ...