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)
A and D
let me know if you want an explanation its a lot to type
Answer:
Step-by-step explanation:
The given inequality is
Add 4 to both sides of the first inequality and subtract 5 from both sides of the second inequality.
We simplify to get:
Divide through the first inequality by 4 and the second by 9.
Answer:
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
Step-by-step explanation:
sin(2x) + sin(4x) = 0
Use double angle formula.
sin(2x) + 2 sin(2x) cos(2x) = 0
Factor.
sin(2x) (1 + 2 cos(2x)) = 0
Solve.
sin(2x) = 0, cos(2x) = -½
2x = 0, 2π/3, π, 4π/3, 2π, 8π/3, 3π, 10π/3
x = 0, π/3, π/2, 2π/3, π, 4π/3, 3π/2, 5π/3
