Convert logx y = 1/2 to exponential form.
1 answer:
Answer:
Exponential form: y = x^½
Step-by-step explanation:
Given
Required:
The exponential form
To convert to an exponential function, we have to take exponents of both sides using the base of the logarithm function.
This gives us
Since the base of the exponential function and the logarithm is the same (x), they'll cancel out one another
This leaves us with
Hence, the exponential form of the expression
is
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The given triangles ΔDOA and ΔABC are right triangles that have a
common vertex at point <em>A</em>.
- <u>ΔDOA is similar to ΔABC, and </u><u>∠AEC</u><u> is equal to </u><u>∠ABC,</u><u> therefore, ∠AEC = ∠ODA</u>
Reasons:
The given parameters are;
The diameter of the circle with center <em>O</em> = AB
DO ⊥ AB (DO is perpendicular to AB)
Required:
Prove that ∠AEC = ∠ODA
A two column proof is presented as follows;
Statement Reason
1. AB is the diameter of circle <em> </em> 1. Given
2. DO is perpendicular to AB <em> </em> 2. Given
3. ∠DOA = 90° <em> </em> 3. Definition of DO ⊥ AB
4. ∠BCA = 90° <em> </em> 4. Thales theorem
5. ∠BCA ≅ ∠BCA <em> </em> 5. Reflexive property
6. ΔDOA ~ ΔABC <em> </em> 6. AA similarity postulate
7. ∠ABC ≅ ∠ODA <em> </em> 7. CASTC
8. ∠ABC = ∠ODA <em> </em> 8. Definition of congruency
9. ∠AEC ≅ ∠ABC <em> </em> 9. Angles in the same segment
10. ∠AEC = ∠ABC <em> </em> 10. Definition of congruency
11. ∠AEC = ∠ODA <em> </em> 11. Transitive property of equality
In statement 6, ΔDOA is similar to ΔABC by Angle-Angle, AA, similarity
postulate, therefore, the three angles of ΔDOA are congruent to the three
angles of ΔABC.
Therefore ∠ABC ≅ ∠ODA by Corresponding Angles of Similar Triangles
are Congruent, CASTC.
Learn more about circle theorem here: