1. ## log 5

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

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

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

2. 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 $\displaystyle log_{2} (\frac{1}{4})=-2$ in exponential form
3. write $\displaystyle 81^{\frac{3}{4}}=27$ in logarithmic form
If you have a logarithmic equation
$\displaystyle \log_b x = y$,
then the corresponding exponential form is
$\displaystyle b^y = x$.

4. what is x in the equation $\displaystyle log_{\frac{1}{4}}x=-2$
Change the equation into exponential form.

01

3. 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
$\displaystyle \log_b x = y$,
then the corresponding exponential form is
$\displaystyle b^y = x$.

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

4. 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
$\displaystyle \log_b x = y$,
then the corresponding exponential form is
$\displaystyle b^y = x$.

Change the equation into exponential form.

01
for 2 i get $\displaystyle 2^-2=1/4$

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

for 4 i get $\displaystyle x=1/16$

3