Answer: proof below
<u>Step-by-step explanation:</u>
Use the Difference formula for sin:
sin (A - B) = sin(A)·cos(B) - cos(A)·sin(B)
sin (180° - θ) = sin(180°)·cos(θ) - cos(180°)·sin(θ)
= 0 · cos(θ) - -1 · sin(θ)
= 0 - -sin(θ)
= + sin(θ)
sin (180° - θ) = sin(θ)
Answer:
log₅(3125) = 5
Step-by-step explanation:
Given:
log₅(3125)
Now,
using the property of log function that
logₐ(b) =
thus,
Therefore, applying the above property, we get
⇒ (here log = log base 10)
now,
3125 = 5⁵
thus,
⇒
Now,
we know from the properties of log function that
log(aᵇ) = b × log(a)
therefore applying the above property we get
⇒
or
⇒ 5
Hence,
log₅(3125) = 5