Properties of Logs
logb(x/y) = log<span>bx</span> - log<span>by</span>.
therefore
log5 (4/7)= log5 (4)- log5 (7)
<span>Solve log 5 (4) and log 5 (7) with the base change of the logarithm</span>
<span>log 5 4 = log 4 / log 5 </span>
Use the calculator:
<span>
<span>log 5 4 =0.8613531161
</span></span>
log 5 7 = log 7 / log 5
<span>log 5 7 =1.2090619551</span>
<span>log5 (4/7)= log5
(4)- log5 (7)=-0.347708839</span>
Given:
To find:
The exact value of cos(u-v) if both angles are in quadrant 3.
Solution:
In 3rd quadrant, cos and sin both trigonometric ratios are negative.
We have,
Now,
On further simplification, we get
Similarly,
Now,
Therefore, the value of cos (u-v) is 0.1872.
The side lengths are 2 units and 4 units. Do you need work?
Answer =-3 or -3/1
You can either do rise/run
Or you can find two points on the line and do (y2-y1)/(x2-x1)
Two points on the line are (-1,2) and (-3,-4)
X1=-1 Y1=2
X2=-3 Y2=-4
(y2-y1)/(x2-x1) = (-4-2)/(-3-(-1)) =(-6)/(-3+1)
=-6/-2 = -3
So slope =-3/1 or -3 (same thing)
