Logarithmic Applications

What is the domain of the given function (graph it): f(x) = log (x + 5) - 2

• {x | x > - 5}

• {x | x > 5}

• {x | x > - 2}

• {x | x > 2}

• 3 (log b - log a)

• log 3b - log a

• 3 log b - log a

• 3 log b + log a

• 62.8 minutes
• 82.6 minutes
• 25.4 minutes
• 77.4 minutes

Decibels (dB) are defined by the equation; 10log [ I / I_o ] , where I_o = 10⁻¹² , the intensity of a barely audible sound. Use the formula to determine the loudness in dB of a jackhammer, which measures an intensity of 10⁻² .

• -10 dB

• 10 dB

• 20 dB

• 100 dB

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

Log with a base "e" (log_e) is the same thing as...

• "e"

• Natural Logarithm (LN)

• Common Logarithm (Log)

• Natural Log, base "e"
  LN_e

In 1935 Charles Richter defined the magnitude of earthquakes to be M = log [I / s] where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicenter of the earthquake) and S is the intensity of a "standard earthquake" (whose amplitude is 1 micron equal to 10^-4 cm). In 1985
What is the magnitude of an earthquake with a seismographic reading of 79432 cm (when measured 100 km from the epicenter) rounded to the nearest tenth?

• 1.2

• 5.5

• 8.1

• 8.9

Use the mathematical model for power gain: G = log [P_o / P_i ]¹⁰ where P_o is the output power in watts and P_i is the input power in watts. Determine the power gain G in decibels, for an amplifier with an output P_o of 20 watts and an input P_i of 1.6 watts. Round to five decimal places if necessary.

• 11.9691 dB

• 10.9691 dB

• 15.0515 dB

• 12.64818 dB

log₂32 = 5

• 2^-5 = 32

• 2³² = 5

• 2⁵ = 32

• 32⁵ = 2

log₄ x = 3

• 4

• 12

• 32

• 64