To answer this, first try to answer thexfollowing: what is x in this equation? 9 = 3
what is x in this equation? 8 = 2x
• Basically, logarithmic transformations ask, “a number, to what power equals another number?”
• In particular, logs do that for specific numbers under the exponent. This number is called the base.
• In your classes you will really only encounter logs for two bases, 10 and e.
Log base 10
We write “log base ten” as “log10” or just “log” for short and we define it like this:
If y=10x So, what is log (10x) ?
then log(y)=x
log (10x) = x 10log(x) = x
How about 10log(x)
More examples: log 100 =
log (105)=
?
2 5
• The point starts to emerge that logs are really shorthand for exponents.
• Logs were invented to turn multiplication problems into addition problems.
Lets see why.
log (102) + log (103) = 5, or log (105)
B/h=3/8
8b=3h
8/3b=h
P=2(h+b)
P=138.6
138.6=2(h+b)
divide both sides by 2
69.3=h+b
suub (8/3)b for h
69.3=(8/3)b+b
times both sides by 3 to get rid of fraction
207.9=8b+3b
207.9=11b
divide both sides by 11
18.9=b
sub back
(8/3)b=h
(8/3)18.9=h
50.4=h
area=height times base
aera=50.4 times 18.9
aera=952.56 cm²
1. base=18.9 cm
2. height=50.4 cm
3. area=952.56 cm²
Answer:
cx +cy = a² + b²
Step-by-step explanation:
In the end, he wants to show that c² = a²+b², so he will want to form the sum a²+b². That sum can be formed by adding the expressions for a² and b² just found:
cx +cy = a² + b² . . . . . . . Todd's next step
__
Then the following steps are ...
c(x+y) = a² + b²
c² = a² + b²
Answer:
= 5 − 101i
Step-by-step explanation:
2i(A ∙ E) − C + G
=
2i(-3 − 4i)(8 − 8i) − (13 + i) + (2 + 12i)
=
2i(-24 + 24i − 32i + 32i2) − (13 + i) + (2 + 12i)
=
2i(-24 − 8i − 32) − (13 + i) + (2 + 12i)
=
2i(-56 − 8i) − (13 + i) + (2 + 12i)
=
(-112i − 16i2) − (13 + i) + (2 + 12i)
=
(16 − 112i) − (13 + i) + (2 + 12i)
=
(16 − 112i) + (-13 − i) + (2 + 12i)
=
(16 − 13 + 2) + (-112i − i + 12i)
=
(16 − 13 + 2) + (-112 − 1 + 12)i
= 5 − 101i
