The expanded logarithm of log 2 x³y⁻² is = log 3 + 3 log x - 2 log y.
What is a logarithmic function?
A logarithmic function in mathematics is defined as the function which is the inverse of the exponential function. It is denoted by using the word log. For example log 10 = 1
Expanding the given logarithm: log 2 x³y⁻²
Given logarithmic expression is log 2 x³y⁻²
Applying given properties of logarithmic function;
log a + log b = log (ab)
2 log a = log a^2
Now, log 2 x³y⁻² = log 3 + log x³ + log y⁻²
= log 3 + 3 log x - 2 log y
Hence, the expanded logarithm of log 2 x³y⁻² is = log 3 + 3 log x - 2 log y.
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Answer:
1. ∠1 = 120°
2. ∠2 = 60°
3. ∠3 = 60°
4. ∠4 = 60°
5. ∠5 = 75°
6. ∠6 = 45°
Step-by-step explanation:
From the diagram, we have;
1. ∠1 and the 120° angle are corresponding angles
Corresponding angles are equal, therefore;
∠1 = 120°
2. ∠2 and the 120° angle are angles on a straight line, therefore they are supplementary angles such that we have;
∠2 + 120° = 180°
∠2 = 180° - 120° = 60°
∠2 = 60°
3. Angle ∠3 and ∠2 are vertically opposite angles
Vertically opposite angles are equal, therefore, we get;
∠3 = ∠2 = 60°
∠3 = 60°
4. Angle ∠1 and angle ∠4 an=re supplementary angles, therefore, we get;
∠1 + ∠4 = 180°
∠4 = 180° - ∠1
We have, ∠1 = 120°
∴ ∠4 = 180° - 120° = 60°
∠4 = 60°
5. let the 'x' and 'y' represent the two angles opposite angles to ∠5 and ∠6
Given that the two angles opposite angles to ∠5 and ∠6 are equal, we have;
x = y
The two angles opposite angles to ∠5 and ∠6 and the given right angle are same side interior angles and are therefore supplementary angles
∴ x + y + 90° = 180°
From x = y, we get;
y + y + 90° = 180°
2·y = 180° - 90° = 90°
y = 90°/2 = 45°
y = 45°
Therefore, we have;
∠4 + ∠5 + y = 180° (Angle sum property of a triangle)
∴ ∠5 = 180 - ∠4 - y
∠5 = 180° - 60° - 45° = 75°
∠5 = 75°
6. ∠6 and y are alternate angles, therefore;
∠6 = y = 45°
∠6 = 45°.
Answer:
4.5
Step-by-step explanation:
Answer:
Answer: D
Step-by-step explanation:
I took the test and got it right i promise
80 miles because if 1=20 then 2=40 3=60 4=80