# (log3 x)^2+2log3x-24=0

## Answers

If you are not satisfied with the answer or you can’t find one, then try to use the search above or find similar answers below.

Find similar answersMathematics, added 2021-03-01 23:15:24

What is the surface are of the container of oatmeal shown below? use 3.14 for pi ...

Mathematics, added 2021-03-01 22:07:46

What is the surface are of the container of oatmeal shown below? use 3.14 for pi ...

Mathematics, added 2021-02-28 12:52:45

The slope of BY is -1/5, and BYllJE What is the slope of JE? -5 -1/5 1/5 5 ...

Mathematics, added 2021-02-28 11:20:45

The slope of BY is -1/5, and BYllJE What is the slope of JE? -5 -1/5 1/5 5 ...

Mathematics, added 2021-02-27 21:17:05

Answered by

exordiumxAnswers: x = 1/729 or x = 81 ====== (log₃ x)² + 2log₃ x - 24 = 0 Notice how this seems to form some sort of quadratic equation. There is a tern with a variable that is squared log₃ x)², then a term with the same variable of the first degree (2log₃ x) and then a constant -24. This looks like ax² + bx + c = 0 Let u = log₃ x. Then this can be written as (log₃ x)² + 2log₃ x - 24 = 0 ⇒ (u)² + 2u - 24 = 0 We can solve this by factoring. Find two numbers that multiply to get -24 and add to get 2. These two numbers are 6 and -4. Therefore, the left-hand side factors into (u + 6)(u - 4) = 0 By the zero factor property, we find solutions by setting the factors to equal zero and then combining the solutions. So u + 6 = 0 or u - 4 = 0 Back-substituting u = log₃ x, we get log₃ x + 6 = 0 or log₃ x - 4 = 0 Isolating the logarithmic term log₃ x = -6 or log₃ x = 4 Use definition of the logarithm to convert these into exponential form. Since logₓ(a) = b ⇔ a = xᵇ, we convert so that these equations turn into x = 3⁻⁶ or x = 3⁴ x = 1/729 or x = 81 Check your solutions by putting them in the original equation. Doing that, both sides of the equation (log₃ x)² + 2log₃ x - 24 = 0 result in 0, indicating that these two numbers are the solutions to the given equation.