Common and Natural Logarithms

Common and Natural Logarithms

Use a calculator to estimate log 15.


1.1761

1.5

0.6667

2.708

Use a calculator to estimate ln 3


0.4771

20.0855

1.0986

1000

Use a calculator to estimate e2.3.


0.8329

9.9742

199.5262

0.3617

Estimate the solution to the exponential equation using logarithms.

7x = 16


1.1293

0.8451

1.2041

1.4248

Use logarithms to estimate the solution to the exponential inequality.

7p + 2 ≤ 135 – p


p ≥ -14.4303

p ≤ 0.2688

p ≤ 1.9803

p ≤ 7.6001

Use a calculator to estimate log4 30.


1.4771

3.4012

0.6021

2.4534

Which of the following is equal to fraction numerator ln space 15 over denominator ln space a end fraction? Assume a ≠ 1


log 15 – log a

loga 15

log15 a

ln 15 – ln a

Write the logarithmic equation in exponential form.

ln 16 ≈ 2.7726


e16 ≈ 2.7726

102.7726 ≈ 16

e2.7726 ≈ 16

1016 ≈ 2.7726

Solve the equation. Round to the nearest ten-thousandth.

3ex – 1 = 0


x = 1.0986

x = -1.0986

x = -0.9102

x = 0.9102

Solve the inequality. Round to the nearest ten-thousandth.

e4x ≥ 16


x ≥ 0.6931

x ≥ 2

x ≥ 4

x ≥ -1.2274