Rewrite the following as a single logarithm. Please show ALL work! 4logx+logy-1/2logz
2 answers:
Answer:
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Work Shown:
I'm going to use the following rules
Rule 1: log(x)+log(y) = log(x*y)
Rule 2: log(x)-log(y) = log(x/y)
Rule 3: y*log(x) = log(x^y)
Rule 4: x^(1/2) = sqrt(x) ... where 'sqrt' stands for 'square root'
Using those rules, we get...
4*log(x)+log(y) - (1/2)*log(z)
log(x^4)+log(y) - log(z^(1/2)) <<-- using rule 3
log(x^4)+log(y) - log(sqrt(z)) <<-- using rule 4
log(x^4*y) - log(sqrt(z)) <<-- using rule 1
log[ (x^4*y)/(sqrt(z)) ] <<-- using rule 2
(if this font is too small then try zooming in, or you can check out the attached image which shows the answer in bigger font)
---------------------------------
Work Shown:
I'm going to use the following rules
Rule 1: log(x)+log(y) = log(x*y)
Rule 2: log(x)-log(y) = log(x/y)
Rule 3: y*log(x) = log(x^y)
Rule 4: x^(1/2) = sqrt(x) ... where 'sqrt' stands for 'square root'
Using those rules, we get...
4*log(x)+log(y) - (1/2)*log(z)
log(x^4)+log(y) - log(z^(1/2)) <<-- using rule 3
log(x^4)+log(y) - log(sqrt(z)) <<-- using rule 4
log(x^4*y) - log(sqrt(z)) <<-- using rule 1
log[ (x^4*y)/(sqrt(z)) ] <<-- using rule 2
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Answer:
Option A is correct
The only figure after composition of to figure R is Figure H
Step-by-step explanation:
From the given figure in R;
The coordinates in Figure R ;
(1 , -1) , (2, -2) ,(4, -2) ( 0, -4)
Composite function defined as when one function is substituted into another function.
To Apply the composition to figure R;
First apply the Reflection in Figure R;
The rule of reflection is given by:
By applying the rule of reflection in Figure R ,
then, the coordinates becomes;
(1 , -1) (1, 1)
(2 , -2) (2, 2)
(4 , -2) (2, 4)
(0, -4) (4, 0)
Now, apply the translation
Translation : It is a type of transformation that moves each point in a figure the same distance in the same direction.
then,
the rule of translation is:
Apply the rule of translation on coordinates (1,1) , (2,2), (2,4) and (4,0)
then
(1 , 1) (1+0 1+3) =(1,4)
(2, 2) (2+0 2+3) =(2, 5)
(2, 4) (2+0 4+3) =(2 ,7) and
(4, 0) (4+0 0+3) =(4 ,3)
Then, the only figure after composition of to figure R is Figure H