log 5

**william** · July 25th 2009, 02:35 PM

1. what is the logarithmic equation with the following transformations

shifted 4 units left
shifted 3 units up
vertically compressed by 1/3
horizontal stretch by 3

2. write $log_{2} (\frac{1}{4})=-2$ in exponential form

3. write $81^{\frac{3}{4}}=27$ in logarithmic form

4. what is x in the equation $log_{\frac{1}{4}}x=-2$

**yeongil** · July 25th 2009, 03:13 PM

Originally Posted by william

1. what is the logarithmic equation with the following transformations

shifted 4 units left
shifted 3 units up
vertically compressed by 1/3
horizontal stretch by 3

1) We've gone over transformations before, william.
Shifting to the left means that f(x) changes to f(x + c).
Shifting upwards means that f(x) changes to f(x) + c.
A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

Apply these transformations, one after another, to f(x) = log(x).

2. write $log_{2} (\frac{1}{4})=-2$ in exponential form
3. write $81^{\frac{3}{4}}=27$ in logarithmic form

If you have a logarithmic equation
$\log_b x = y$ ,
then the corresponding exponential form is
$b^y = x$ .

4. what is x in the equation $log_{\frac{1}{4}}x=-2$

Change the equation into exponential form.

01

**william** · July 25th 2009, 03:23 PM

Originally Posted by yeongil

1) We've gone over transformations before, william.
Shifting to the left means that f(x) changes to f(x + c).
Shifting upwards means that f(x) changes to f(x) + c.
A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

Apply these transformations, one after another, to f(x) = log(x).

If you have a logarithmic equation
$\log_b x = y$ ,
then the corresponding exponential form is
$b^y = x$ .

Change the equation into exponential form.

01

thanks,for the equation i get f(x)= log(x+4)+3, i can't get the rest

**william** · July 25th 2009, 03:28 PM

Originally Posted by yeongil

1) We've gone over transformations before, william.
Shifting to the left means that f(x) changes to f(x + c).
Shifting upwards means that f(x) changes to f(x) + c.
A vertical shrink means that f(x) changes to c*f(x), where c is in 0 < c < 1.
A horizontal stretch means that f(x) changes to f(x/c), where c > 1.

Apply these transformations, one after another, to f(x) = log(x).

If you have a logarithmic equation
$\log_b x = y$ ,
then the corresponding exponential form is
$b^y = x$ .

Change the equation into exponential form.

01

for 2 i get $2^-2=1/4<br />$

for 3 i get $log_{3/4}27=81$

for 4 i get $x=1/16<br />$

3

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