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)
Answer:
-7
Step-by-step explanation:
Answer:
5 km
Step-by-step explanation:
It helps to draw a diagram.
The triangle between Stamford, Newport, and Amanda's house is a right triangle with one leg of length 12 and hypotenuse 13. The Pythagorean theorem can be used to find the remaining leg:
13² = 12² + (distance to Newport)²
169 -144 = (distance to Newport)²
√25 = 5 = distance to Newport
Newport is 5 km from Amanda's house.
_____
It can be useful to remember this right triangle. 5-12-13 right triangles show up in a number of algebra and geometry problems.
Answer:
they are both divisible by 4
so you could write
4 (5 + 4)
Step-by-step explanation:
Keep in mind that a coordinate is in the form (x, y), so if you plug those values into the equation y=3x+1, you get 1=3(4)+1, simplified to 1=13, which is an untrue statement. However, I'm assuming you mean that the value of y is 4 and x is 1, which would be written as (1, 4). This would be the solution to this equation because 4=3(1)+1 is 4=4 which is a true statement.
