MATH SOLVE

3 months ago

Q:
# Use the method from the Example to approximate the solution to the equations below to two decimal places.6^x = 1,000

Accepted Solution

A:

Answer:x = 3.85 Step-by-step explanation:Given equation:6ˣ = 1,000now,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 thatlog(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) = 1log(2) = 0.3010 log(3) = 0.4771 Thus,⇒ x × [0.3010 + 0.4771 ] = 3 × 1or⇒ x × 0.7781 = 3or⇒ x = 3.85