Logarithms – An Introduction Check for Understanding – 3103.3.16 Prove basic properties of logarithms using properties of exponents and apply those properties.

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Presentation transcript:

Logarithms – An Introduction Check for Understanding – Prove basic properties of logarithms using properties of exponents and apply those properties to solve problems. Check for Understanding – Know that the logarithm and exponential functions are inverses and use this information to solve real-world problems.

What are logarithms? log·a·rithm : noun the exponent that indicates the power to which a base number is raised to produce a given number Merriam-Webster Online (June 2, 2009)

What are logarithms used for? pH Scale Richter Scale Decibels Radioactive Decay Population Growth Interest Rates Telecommunication Electronics Optics Astronomy Computer Science Acoustics … And Many More!

My calculator has a log button… why can’t I just use that? The button on your calculator only works for certain types of logarithms; these are called common logarithms.

Try These On Your Calculator log 2 45 log  X 

What’s the difference? The log button on the calculator is used to evaluate common logarithms, which have a base of 10. If a base is not written on a logarithm, the base is understood to be 10. log 100 is the same as log

The logarithmic function is an inverse of the exponential function.

Logarithm with base b The basic mathematical definition of logarithms with base b is… log b x = y iff b y = x b > 0, b ≠ 1, x > 0

Write each equation in exponential form. 1.log 6 36 = =36 2. log = 1 5 =5125

Write each equation in logarithmic form = 8 2 = = 1 49 log =–2 log8 7

Evaluate each expression 5. log 4 64 = x6. log 5 625= x 4 x = 64 5 x = x = 4 3 x = 3 5 x = 5 4 x = 4

Evaluate each expression 7.log log 3 9. log log 11 1

Evaluate each expression 7.log log 3 –4 9. log 8 4 ⅔ 10. log

Solve each equation 11. log 4 x = 3 12.log 4 x = = x 64 = x x = 8 4= x

Evaluate each expression 13. log 6 (2y + 8) = log b 16 = log 7 (5x + 7) = log 7 (3x + 11) 16. log 3 (2x – 8) = log 3 (6x + 24)

Evaluate each expression 13. log 6 (2y + 8) = log b 16 = log 7 (5x + 7) = log 7 (3x + 11) log 3 (2x – 8) = log 3 (6x + 24)