Warmup Solve log5 6 + 3 log5 x = log5 48.

6-7 Common Logarithms Solve exponential and logarithmic problems with common logarithms. Evaluate logarithmic expressions with the change of base formula

Logarithms with a base of 10 are called common logarithms Logarithms with a base of 10 are called common logarithms. The 10 is usually not written, that is, log10 x is written as log x. Most calculators have a LOG  key on the face of the calculator for evaluating common logarithms. Use a calculator to evaluate each expression to the nearest ten-thousandth.

Base 10 Common logs are used in the measurement of sound. where L is measured in decibels, I is the intensity of the sound, and m is the minimum intensity of sound detectable by the human ear. For most purposes, we will define m to be 1.

22. Loretta had a new muffler installed on her car 22. Loretta had a new muffler installed on her car. The noise level of the engine dropped from 85 decibels to 73 decibels. How many times the minimum intensity of sound detectable by the human ear was the car with the old muffler, if m is defined to be 1? b) How many times the minimum intensity of sound detectable by the human ear is the car with the new muffler? Find the percent of decrease of the intensity of the sound with the new muffler. 𝐿=10 log 𝐼 𝑚

If both sides of an exponential equation can’t easily be re-written as powers with the same base, you can solve by taking the logarithm of both sides! (write that down)

Solve. Round to nearest ten thousandth.

Solve. Round to nearest ten thousandth.

When you change base, the new base can be any b you want When you change base, the new base can be any b you want. Most times you would just choose base 10, since it is easily accessible from your calculator keys on the front.

Express each logarithm in terms of common logarithms Express each logarithm in terms of common logarithms. Then approximate the value to the nearest ten thousandth.

Solve. Round to nearest ten thousandth.

Solve. Round to nearest ten thousandth.