Question

Explain how to solve 3^(x − 4) = 6 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth.

Answer 1

Given:

3^(x − 4) = 6

To find:

Solution to the given expression using change of base formula

Answer:

• The given expression is 3^(x − 4) = 6
• Taking log on both sides, we get -
• log(3^(x − 4)) = log6
• (x - 4) log3 = log6
• x - 4 = log6/ log3
• x - 4 = $log_{3} 6$  (∵ change of base formula)
• x - 4 = 1.631
• x = 5.631

Thus x = 5.631 is the answer in the nearest thousandth.

Answer 2

Answer: x = 5.631

Step-by-step explanation:

Given:

3^(x − 4) = 6

To find:

Solution to the given expression using change of base formula

Answer:

The given expression is 3^(x − 4) = 6

Taking log on both sides, we get -

log(3^(x − 4)) = log6

(x - 4) log3 = log6

x - 4 = log6/ log3

x - 4 =   ( change of base formula)

x - 4 = 1.631

x = 5.631

Thus x = 5.631 is the answer in the nearest thousandth.