Flashcards
Logarithm Basics
Cards in this deck (21)
- 1Graph of y=2^xAsymptopic to x-axis
- 2Logarithm notation:b^p = a <=> log(b)a=p
- 3If 2^3=8, how do we write this in logarithm form?log(2)8=3
- 4log(e) is the same as....In (natural logarithm)
- 5Log(10) is the same as....Log (on its own)
- 6log(a)xy is the same as.....log(a)x + log(a)y
(as a^x x a^y = a^x+y) - 7log(a)x/y is the same as.....log(a)x - log(a)y
(as a^x/a^y = a^x-y) - 8log(a)x^y is the same as.....ylog(a)x
(as (a^x)^y = a^xy) - 9log(a)1 = .....0
(as a^0 = 1) - 10log(a)a = .....1
(as a^1 = a) - 11log(a)1/x = .....-log(a)x
- 12Rewrite log(a)x^3 x y^1/2 / 3 as a 3 log expressionslog(a)x^3 + log(a)y^1/2 - log(a)3
= 3log(a)x + 1/2log(a)y - log(a)3 - 13Rewrite 2log(a)m - 3log(a)n + log(a)7 as a single expressionlog(a)m^2 - log(a)n^3 + log(a)7
= log(a)7m^2 / m^3 - 14Rewrite 2log(a)x + 3 - log(a)2 as a single expression2log(a)x + 3log(a)a - log(a)2
= log(a)x^2 + log(a)a^3 - log(a)2
= log(a)(x^2 x a^3 / 2) - 15Solve 2^x = 5x=log(2)5 , x= 2.32
- 16Solve 3 x 2^x = 151. Divide both sides by 3 to get 2^x = 5 and do x=log(2)5 , x=2.32
2. State: log(2)3 x 2^x = log(2)15 , log(2)3 + log(2)2^x = log(z)15 , x=log(2)15 - log(2)3 , x=2.32 - 17Find k when : 2^x = 3^kxlog(3)2^x = log(3)3^kx , xlog(3)2 = kx , xlog(3)2 - kx = 0 , x(log(3)2 - k) = 0
x=0 or log(3)2 = k
OR
(2)^x = (3^k)^x , x=0 or 2=3^k - 18Solve : 5 x 4^x = 3 x 5^xlog(4)5 x 4^x = log(4)3 x 5^x
log(4)5 + log(4)4^x = log(4)3 + log(4)5^x
log(4)5 + x = log(4)3 + xlog(4)5
log(4)5 - log(4)3 = xlog(4)5 - x
log(4)5 - log(4)3 = x(log(4)5 - 1)
(log(4)5 - log(4)3) / log(4)5 - 1 = x
x=2.29 - 19Solve : 3 x e^x = 2^xIn(3e^x) = In(2^x)
In(3) + In(e^x) = x(In(2))
In(3) = xIn(2) - x
In(3) = x(In(2) - 1)
In(3) / In(2) - 1 = x - 20Solve : e^kx = 3^xIn(e^kx) = In(3^x)
kx = xIn(3)
kx - xIn(3) = 0
x(k - In(3)) = 0
x=0 or k=In(3) - 211. 1.8^x = 0.4 (find x) 2. 0.4^5x-4 = 2 (find x) 3. 5e^3f = 11 (find f)1. log(1.8)0.4 = -1.56
2. log(0.4)2 = 5x-4 , 5x-4=-0.75, x=0.95
3. In(5)11 = 3f, 3f=0.92, f = 0.31