Solving equations Solve the following equatio...

Question

Solving equations Solve the following equations.

3(ˣ³⁻⁴) = 15

Accepted Answer

Hi everyone, let's take a look at this practice problem. This process is to find the value of X in the equation of 4 rates to the quantity of 3 X minus 1, and quantity is equal to 65. We're given 4 possible choices as our answers. For choice A, we have X is equal to the natural log of 65 divided by the natural log of 2, plus 1 divided by 3. For choice B, we have X's equal to the natural log of 65, divided by the quantity of 6 multiplied by the natural log of 2 in quantity minus 1 divided by 3. For choice C, we have X is equal to the natural log of 65, divided by the quantity of 6 multiplied by the natural log of 2 in quantity, plus 1 divided by 3. And for choice D, we have X is equal to the natural log of 65, divided by the quantity of 6 multiplied by the natural log of 2. Now we're asked to find the value of X in the equation of 4 rates to the quantity of 3 x minus 1 and quantity is equal to 65. So our first step is to rewrite 4 as 2 squad. So then our equation will become 2 raised to the quantity of 2 multiplied by the quantity of 3 X minus 1 in quantity is equal to 65. So now I want to get the X out of the X component, and to do that, we're going to use logarithms. So recall your power rule for logarithms, that is that the natural log of the quantity of a raised to the power B is equal to B multiplied by the natural log of A. So, using this rule, we're going to take the natural log of both sides of our equation here. And doing so, we will get 2 multiplied by the quantity of 3 X minus 1 in quantity, multiplied by the natural log of 2 is equal to the natural log of 65. So now we just need to isolate X. The first step is to divide both sides of your equation by 2 multiplied by the natural log of 2. And in doing so, We will get 3 X minus 1 is equal to the natural log of 65, divided by the quantity of 2 multiplied by the natural log of 2. I now need to add 1 to both sides of the equation, and so I will get 3 X. It's equal to the natural log of 65 divided by the quantity of 2 multiplied by the natural log of 2 in quantity plus 1, and then finally just divide both sides by 3. And so I will have X is equal to the natural log of 65, divided by the quantity of 2 multiplied by 3, which is 6, multiplied by the natural log of 2 in quantity, plus 1 divided by 3. So this is the answer that we are looking for, and if I compare our calculated answer to the answer choices, the correct answer choice turns out to be answer choice C. So I hope that this explanation has been useful, and I'll see you in the next video.

Solving equations Solve the following equations.

3(ˣ³⁻⁴) = 15

Key Concepts

Exponential Equations

Isolating the Variable

Properties of Equality

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