Find the equation of the inverse function..Logarithm.

**NotSoBasic** · May 25th 2009, 08:01 PM

1a)
$y=log_5 x$
$x=log_5 y$
$5^x=y$
$y=5^x$
$f^{-1} (x)=5^x$

b)
$y=-log_5 (-x)$
$x=-log_5 (-y)$
$-5^x=-y$
$-y=-5^x$
$f^{-1} (-x)=-5^x$

Do those seem correct?

**pickslides** · May 25th 2009, 08:48 PM

Originally Posted by NotSoBasic

1a)
$y=log_5 x$
$x=log_5 y$
$5^x=y$
$y=5^x$
$f^{-1} (x)=5^x$

b)
$y=-log_5 (-x)$
$x=-log_5 (-y)$
$-5^x=-y$
$-y=-5^x$
$f^{-1} (-x)=-5^x$

Do those seem correct?

I agree with the first question.

I think the 2nd question should be
$y=-log_5 (-x)$
$x=-log_5 (-y)$
$-x=log_5 (-y)$
$5^{-x}=-y$
$-y=5^{-x}$
$y=-5^{-x}$
$f^{-1}=-5^{-x}$

**Soroban** · May 25th 2009, 08:55 PM

Hello, NotSoBasic!

The first one is correct . . .

$b) \;\;y \:=\:-\log_5 (-x)$

We have: . $x \:=\:-\log_5(-y)$

Switch sides: . $-\log_5(-y) \:=\:x$

Multiply by -1: . $\log_5(-y) \:=\:-x$

Exponentiate: . $-y \:=\:5^{-x}$

Multiply by -1: . $y \:=\:-5^{-x}$

Therefore: . $f^{-1}(x) \:=\:-5^{-x}$

Edit: too slow again . . .
.

**NotSoBasic** · May 25th 2009, 09:28 PM

Those make more sense, thanks guys!

**pickslides** · May 25th 2009, 09:30 PM

Originally Posted by Soroban

Edit: too slow again . . .

happens often to me as well.

Thread: Find the equation of the inverse function..Logarithm.

LinkBack

Thread Tools

Display

Find the equation of the inverse function..Logarithm.

Similar Math Help Forum Discussions

Need help with Logarithm and Inverse Function

find inverse function

Finding the inverse function of a logarithm

Help me find the inverse of this function!

help me to find the inverse function

Search Tags