6 3 Logs fguilbert Review of Exponent Rules
6. 3 Logs fguilbert
Review of Exponent Rules To multiply powers of the same base, add the exponents. x x x fguilbert x x x
Division To divide powers of the same base, subtract the exponents. fguilbert
Powers &Parenthesis When exponent is outside multiply exponents. Expon applies to each term in ( ) (5 fguilbert 3 X 4 2 Y ) = 25 6 X 8 Y
Negative Exponents -n X -2 5 fguilbert =1 2 5 =1 n X reciprocal + 3 4 -3 = 4 3 3
Zero Exponent 0 X = 1 x=0 0 3 = 1 0 (-7) = 1 fguilbert
Fraction Exponents a fguilbert n/m = 27 1/3 = =3 16 1/4 = =2
4 6 x y ( 4 6 1/3 8 x y ) 4/3 6/3 x y 2 1 1/3 2 2 x x y 2 2 xy fguilbert
Solve: X = 10, 000 4 X = +10 fguilbert
Solve: X 2 = 10 ? ? ? How can we solve this? fguilbert
Exponential Function has an equation in the fo y=b x To obtain the inverse, sw y X and Y. X=b fguilbert y = logb X
Ex. Rewrite 2 5 = 25 log 5 25 = 2 fguilbert
log 2 16 = 4 base exponent Write in exponent form. 4 2 base fguilbert = 16 exponent
Solve Rewrite fguilbert log 4 X = 3 3 4 =X 64 = X
Solve Rewrite logx 81 = 4 4 X = 81 4 1/4 (X ) = 81 X =3 Or take the 4 th root each side. fguilbert
Solve: log 2 128 = X X 2 = 128 X 7 2 =2 X=7 fguilbert
Use your calculator for the same example. log 2 128 = X log 128 / log 2 = 7 fguilbert
Evaluate log 4 8 no calc. y 4 =8 we know that 1 4 =4 2 4 = 16 can’t write 4 2 so change 4 to 2 N fguilbert
Evaluate log 4 8 no calc. y 4 =8 2 y (2 ) = 8 2 y 3 (2 ) = 2 Since bases are ar same, exps. 2 y = 3 are =. y = 1. 5 2 y 2 = fguilbert 3 2
Look at that earlier proble X 2 = 10 10 can’t be N written 2. Use LOGS. fguilbert log 2 10 = x log 10 / log 2 = X 3. 322 = X
log 10 / log 2 = X 3. 322 = X Try your calculator watch ( ) or hit enter at the end of the numerator. fguilbert
exp review simplify 3 add exp. fguilbert = 1/3 x 3/4 x 1/3 = 4/12 3/4 = 9/12 13/12 1 1/12
Simplify 3= 1/3 x =x 3/4 x 1 1/12 =X X =X fguilbert
Thought for the day: Mistakes are the portal to discovery. fguilbert
p. 374 # 3 -7, 11, 12, 16 p 380 # 1 -5, 7 -10 fguilbert
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