What is the solution 6^2x=800? round to the nearest tenth

The solution is x = 1.9 to the nearest tenth

Step-by-step explanation:

* Lets revise the meaning of exponential function

- The form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,

  b ≠ 1, and x is any real number

- It has a constant base b

- It has a variable exponent x

- To solve an exponential equation, take the log or ln of both sides,

  and solve for the variable

* Lets solve the problem

∵ 6^2x = 800

- The base is 6 and the variable is 2x

- Insert ㏑ for both sides

∴ ln(6^2x) = ㏑(800)

- There is a rule that ⇒ ㏑(a^b) = b ㏑(a)

∴ 2x ㏑(6) = ㏑(800)

- Divide the both side by ㏑(6) to isolate the variable x

∴ 2x = ㏑(800) ÷ ㏑(6)

- Now divide both sides by 2 to find x

∴ x = [㏑(800) ÷ ㏑(6)] ÷ 2

∴ x = 1.865376 ≅ 1.9 to the nearest tenth

* The solution is x = 1.9 to the nearest tenth

1.87

Step-by-step explanation: