Review Lesson 7.6 COMMON LOGARITHMS by Tiffany Chu, period 3

WHAT ARE COMMON LOGARITHMS? Base 10 logarithms (y=log10x) are called common logarithms We are finding what the exponent is that turns ten to x. Common logarithms are usually written without the subscript as log x You can use the log button on your calculator to evaluate a log expression

INVERSE PROPERTY OF LOGARITHMS & EXPONENTS 10logx = x Common log tells us what exponent turns 10 into x. This means that when you find 10 to the power of the exponent that turns 10 into x, 10 and log10 cancel out, leaving x as the answer.

For all positive numbers a, b, and n, where a and b do not equal 1, CHANGE OF BASE FORMULA For all positive numbers a, b, and n, where a and b do not equal 1, logan = When you are given logan, you can solve it by picking a positive base, b, greater than one and finding the quotient of logbn and logba. logbn logba

USING COMMON LOG TO SOLVE EQUATIONS 4x+3 = 18 1. Put the equation into logarithmic form log418 = x+3 x = -0.9150 2. Use the Change of Base Formula using b = 10 x + 3 = log 18 log 4 - 3 3. Subtract 3 from both sides to isolate x x = log 18 log 4

EXPRESSING IN TERMS OF COMMON LOG 1. Use the Change of Base Formula using b = 10 log(4)2 log 3 x = 2.5347 2. Raise 4 to the second power Write the fraction on your calculator using the Alpha key + y = key and choose the first option OR Find the quotient of the 2 common logs log 16 log 3

7.84x ≥180 PRACTICE PROBLEMS ⅓log527 1. Solve this inequality. Round to the nearest ten-thousandth. HINT! Turn both sides into common logs 7.84x ≥180 2. Express the logarithm in terms of common logarithms. Then approximate its value to the nearest ten-thousandth ⅓log527

x ≥0.6320 ANSWERS TO PRACTICE PROBLEMS 0.6826 log 3 log 5 1. Solve this inequality. Round to the nearest ten-thousandth. HINT! Turn both sides into common logs x ≥0.6320 2. Express the logarithm in terms of common logarithms. Then approximate its value to the nearest ten-thousandth 0.6826 log 3 log 5

THE END AND GOOD LUCK!