Answer:
x = 3.85
Step-by-step explanation:
Given equation:
6ˣ = 1,000
now,
on taking log both sides, we get
⇒ log(6ˣ) = log(1,000)
or
⇒ log(6ˣ) = log(10³)
now we know the property of log function that
log(aᵇ) = b × log(a)
thus, applying the above property, we get
⇒ x × log(6) = 3log(10)
or
⇒ x × log(2×3) = 3log(10)
now,
we have another property of log function as":
log(A) = log(A) + log(B)
therefore,
x × [log(2) + log(3)] = 3log(10)
also,
log(10) = 1
log(2) = 0.3010
log(3) = 0.4771
Thus,
⇒ x × [0.3010 + 0.4771 ] = 3 × 1
or
⇒ x × 0.7781 = 3
or
⇒ x = 3.85
