Solve each exponential equation in Exercises 23–48. Express the s...

Question

Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x=3.91

Accepted Answer

Hello. Today we are asked to sulfur X in the given exponential equation. So the equation given to us is seven race of the power of X is equal to 8.77. Now, in order to sulfur X, we need to find a way to bring down X from the exponents. And in order to do that, we're going to use the exponential rule for for natural logs. And that states that if you have the natural log of a number race of an exponent, You can bring this exponent in front of the natural log as a product. Or in other words the natural log of X to the power of a can be rewritten as a times the natural log of X. And that's what we're going to be doing in this given equation. So let's first take the natural log of both sides of the equation. That's going to give us the natural log of seven to the power of x equal to the natural log of 8.77. Now using our exponential rule, we can take X and put it in front of the natural log of seven. So we can rewrite the left hand side as X times the natural log of seven equal to the natural log of 8.77. Now, in order to get X by itself, we can divide both sides of the equation by the natural log of seven and doing so is going to give us X is equal to the natural log of 8.77 over the natural log of seven. Now this is the answer for X. But keep in mind that the problem asks us to estimate this value to four decimal places. So if you were to plug this into a calculator, you should get the approximate value of 1.1158. And this is going to be the complete solution to X. And with that being said, the answer to this problem is going to be be so. I hope this video helps you in understanding how to solve an exponential equation and I'll go ahead and see you all in the next video.

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Solve each exponential equation in Exercises 23–48. Express the solution set in terms of natural logarithms or common logarithms. Then use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 10^x=3.91

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