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

6^x = 1,000

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