Antagonistic Functions Logarithms
Launching to inverse functions logarithms:<\p>
Inverse functions:<\p>
The inverse of the given function can be described as the undo of the initial clockworks of the ic analysis. All the function has its dead against. But not every inverse is a function.<\p>
Logarithms:<\p>
The deal is a math concept that employed to express the dealings between the variables in easy manner. The following are the some properties in respect to the log functions.<\p>
Properties pertinent to logarithms:<\p>
1.` \log_a a ^x = x, `<\p>
2. `\log_a (x * y)=\log_a x+\log_a y.`<\p>
3.` \log_a \frac}x}}y} = \log_a x - \log_a y.`<\p>
4. `\log_a x ^n= n\log_a deciliter `<\p>
5. `\log_a x=\frac}\log_b x}}\log_b a}`<\p>
6. `e^(log x) = x `<\p>
In this article we are going to see some solved problems and practice problems on opposite side functions logarithms. Problems on Inverse Functions Logarithms:<\p>
Problem 1:<\p>
Find the inverse relative to a logarithms function f(x) = billet 3x<\p>
Solution:<\p>
Escape clause f(x) = post 3x<\p>
We need to find the opposite number of the given assignment.<\p>
On route to find the inverse of the given function, taking exponent towards both edges,<\p>
Before that substitute f(x) = y<\p>
y = log 3x<\p>
`e^y` = `e^(log 3x)`<\p>
We know that `e^logx = x`<\p>
`e^y` = 3x<\p>
Separated at 3 on both sides,<\p>
`(e^y)\3` = `(3x)\3`<\p>
`(e^y)\3` = crux ansata<\p>
x = `(e^y)\3`<\p>
Replace crux gammata = `f^(-1)(christogram)` and y = riddle<\p>
`f^(-1)(x)` = `(e^decasyllable)\3 `<\p>
Answer: The inverse concerning the given thing is `f^(-1)(x) = (e^x)\3 `<\p>
Problem 2:<\p>
Find the inverse of a positive function f(x) = 5 poll 5x<\p>
Solution:<\p>
Given f(the unfamiliar) = 5 log 5x<\p>
We need to find the inverse of the given fixed purpose.<\p>
To find the inverse of the given function, taking exponent on both swelled head,<\p>
Before that vicar general f(x) = y<\p>
y = 5 log 5x<\p>
Divided by 5 on both sides,<\p>
`y\5` = `log 5x`<\p>
`e^(y\5)` = `e^(log 5x)`<\p>
We be friends that `e^logx = x`<\p>
`e^(y\5)` = 5x<\p>
Divided by 5 as for both sides,<\p>
`(e^(y\5))\5` = `(5x)\5`<\p>
`(e^(y\5))\5` = x<\p>
x = `(e^(y\5))\5`<\p>
Replace x = `f^(-1)(x)` and y = x<\p>
`f^(-1)(x)` = `(e^(crisscross\5))\5 `<\p>
Answer: The inverse of the given function is `f^(-1)(x) = (e^(x\5))\5 ` Practice Problems on Inconsistent Functions Logarithms:<\p>
Problems:<\p>
1. Find the antonym respecting a logarithms function f(x) = 3log 6x<\p>
2. Find the inverse of a logarithms employment f(x) = log 10x<\p>
Settling:<\p>
1. The inverse speaking of the eleemosynary function is `f^(-1)(x) = (e^(crux gammata\3))\6 `<\p>
2. The eyeball-to-eyeball of the given function is `f^(-1)(x) = e^(decagon) \ 10 `<\p>
Learn too on about Oblique Asymptote and its Examples. Between, if you have problem on these topics Substance to Words , please browse clever math related websites companion mathcaptain.com, tutorvista.com. Choose share your comments.<\p>
