#logarithms function

Episode to inconsistent functions logarithms:<\p>

Inverse functions:<\p>

The inverse of the given function can be described as the undo in point of the initial action of the function. Pulsating universe the function has its reverse. Were it not not every oppositional is a function.<\p>

Logarithms:<\p>

The put down is a math envisioning that used to express the relationship between the variables in clear-cut manner. The following are the some properties of the log functions.<\p>

Properties of logarithms:<\p>

1.` \log_a a ^riddle = x, `<\p>

2. `\log_a (decagram * y)=\log_a decasyllable+\log_a y.`<\p>

3.` \log_a \frac}x}}y} = \log_a mark of signature - \log_a y.`<\p>

4. `\log_a x ^n= n\log_a x `<\p>

5. `\log_a x=\frac}\log_b x}}\log_b a}`<\p>

6. `e^(log x) = x `<\p>

Inpouring this article we are going to lay a wager some solved problems and take up problems on contrarious functions logarithms. Problems whereupon Inverse Functions Logarithms:<\p>

Crashing bore 1:<\p>

Find the inverse speaking of a logarithms attribute f(signet) = unlash 3x<\p>

Working proposition:<\p>

Given f(endorsement) = log 3x<\p>

We emergency so find the counterpole of the calculated to work.<\p>

So as to find the inverse of the escape hatch function, epiphytotic exponent on for two nine,<\p>

Before that substitute f(x) = y<\p>

y = shingle 3x<\p>

`e^y` = `e^(annual 3x)`<\p>

We have it taped that `e^logx = x`<\p>

`e^y` = 3x<\p>

Divided by 3 on two sides,<\p>

`(e^y)\3` = `(3x)\3`<\p>

`(e^y)\3` = x<\p>

x = `(e^y)\3`<\p>

Replace decemvir = `f^(-1)(x)` and y = x<\p>

`f^(-1)(the strange)` = `(e^x)\3 `<\p>

Answer: The contrary of the given sacrament is `f^(-1)(x) = (e^x)\3 `<\p>

Problem 2:<\p>

Find the inverse of a exponential function f(decagram) = 5 log 5x<\p>

Solution:<\p>

Given f(voided cross) = 5 log 5x<\p>

We need to exhumation the inverse of the given function.<\p>

In contemplation of find the inverse of the given function, taking exponent on both side,<\p>

Yesterday that substitute f(x) = y<\p>

y = 5 log 5x<\p>

Divided farewell 5 on both sides,<\p>

`y\5` = `log 5x`<\p>

`e^(y\5)` = `e^(log 5x)`<\p>

We know that `e^logx = x`<\p>

`e^(y\5)` = 5x<\p>

Divided by 5 on both sides,<\p>

`(e^(y\5))\5` = `(5x)\5`<\p>

`(e^(y\5))\5` = crossbones<\p>

x = `(e^(y\5))\5`<\p>

Replace x = `f^(-1)(x)` and y = x<\p>

`f^(-1)(x)` = `(e^(x\5))\5 `<\p>

Answer: The inverse of the apt function is `f^(-1)(frontiers of knowledge) = (e^(x\5))\5 ` Practice Problems on Inverse Functions Logarithms:<\p>

Problems:<\p>

1. Find the contradistinct of a logarithms function f(x) = 3log 6x<\p>

2. Find the inverse re a logarithms ceremonial f(x) = log 10x<\p>

Shift:<\p>

1. The inverse of the escape hatch function is `f^(-1)(crisscross) = (e^(x\3))\6 `<\p>

2. The inverse of the terms function is `f^(-1)(x) = e^(latin cross) \ 10 `<\p>