Logarithmic Functions 5.5

Logarithms to other bases logb x = a if and only if x = ba. Note: b > 0, and b ≠ 1 The common logarithm of any positive real number x is defined to be the exponent you get when you write x as a power of 10. log x = a IFF x = 10a This is true because log has a base of 10, however, we do not write it the same way we don’t write x = 1x. For example: log 6.3 ≈ 0.8 because 6.3 ≈ 100.8 Logarithms to other bases

Find the decibel level for each sound with the given intensity I of an average car at 70 km/h, I = 106.8I0. Find the decibel level of two stereos, playing the same music simultaneously at 62dB. Ex. 1 & 2

Ex. 3 Write each equation in exponential form. A) log4 16 = 2 B) log 1000 = 3 C) Ex. 3 Write each equation in exponential form.

Natural Logarithm Function ln x = k IFF ek = x **NOTE** The ln eliminates e and vice versa Natural Logarithm Function

Ex. 4 Find the value of x to the nearest hundredth. A) 10x = 100 B) ex = 100 Ex. 4 Find the value of x to the nearest hundredth.

Ex. 5 Find each logarithm. (Do not use a calculator) A) log 100 B) log 0.01 C) log3 9 D) log5 E) ln e2 F) log5 58 Ex. 5 Find each logarithm. (Do not use a calculator)

Ex. 6 Given log 4.17 ≈ 0.6201, find (w/o a calc): HINTS Put given in exp. form & think match You can also match and substitute Use properties of logs C) log 1 4.17 log4.17-1 -1log4.17 -1(.6201) -.6201 A) log 417 log(4.17102) log(10.6201102) log(102.6201) 2.6201 B) log 0.417 4.1710.6201(given exp. form) (10-1) 4.1710.6201(10-1) .417  10-.3799(matches) log (10-.3799) (plug in) -.3799 Ex. 6 Given log 4.17 ≈ 0.6201, find (w/o a calc):

Ex. 7 Solve for x without using a calculator. A) log x = 3 B) log | x | = 3 C) log | x – 1 | = 3 D) log 4 x = 1.5 E) ln x = 1.5 F) ln x = 0 Ex. 7 Solve for x without using a calculator.

Ex. 8 Solve for x using a calculator. A) log x = 0.7 B) ln x = –1.5 C) ex = 5 Ex. 8 Solve for x using a calculator.