Solving equations Solve the following equations.

Question

5(ˣ³) = 29

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says to determine the value of Z in the equation of 7 rates to the quantity of 2 Z and quantity is equal to 50. We have 4 possible choices as our answers. For choice A, we have Z is equal to the natural log of 7 divided by the natural log of 50. Your choice B, we have Z is equal to the natural log of 7, divided by the quantity of 2 multiplied by the natural log of 50. For choice C, we have Z is equal to the natural log of 50 divided by the quantity of 2 multiplied by the natural log of 7. And for choice D we have Z is equal to the natural log of 50 divided by the natural log of 7. Now, we're going to be looking for the uh value of Z in the equation of 7 raised to the quantity of 2 Z in quantity is equal to 50. And what we want to do is get the Z out of the exponent. And to do this, we're going to need to use natural logs. So recall your power property of natural logarithms. And that is that the natural log of the quantity of A rated to the power B is equal to B multiplied by the natural log of A. So, we're going to use this property, and so we're gonna take the natural log of both sides of our equation. And so on the left-hand side, we're going to pull the exponent out in front of the natural log. We'll have 2 multiplied by Z, multiplied by the natural log of 7, and this is equal to the natural log of 50. So now we need to isolate Z by dividing both sides of our equation by the quantity of 2 multiplied by the natural log of 7. And doing so, we will get that Z is equal to the natural log of 50. Divided by the quantity of 2 multiplied by the natural log of 7. So this is the answer that we are looking for. And to compare this to our answer choices, we see that the correct answer choice corresponds to answer choice D. So I hope this explanation has been useful, and I'll see you in the next video.

Solving equations Solve the following equations.

5(ˣ³) = 29

Key Concepts

Exponential Equations

Logarithms

Algebraic Manipulation

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