Question

Use the method from the Example to approximate the solution to the equations below to two decimal places.

6^x = 1,000

Answer 1

x = 3.85

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