Solve each equation. In Exercises 11–34, give irrational solution...

Question

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4.
5^2x + 3(5^x) = 28

Accepted Answer

Solve the following equation for X and provide an exact solution. But we have seven, raise the two X plus two multiplied by seven to the X equals 48. Now, to solve this, I'm going to write this as a quadratic first seven to the two X plus two multiplied by seven to the X minus 48 equals zero. Let's make a substitution here. Let's say are U will equal seven to the XX. We could then rewrite this as U squared plus two, U minus 48 is equals to zero. Not define the factors of this quadratic. Let's find the factors of 48 F 1 48 2, 24 3, 16, 4, 12 and finally six and eight. Now we need these factors to add up to equals two. Now we have a negative 48. So let's say we use eight and six and turn this into a negative six. We can then rewrite this as U minus six, multiplied by U plus eight is equals to zero, U minus six equals zero and U plus eight equals zero. And finally, we can plug our substitution back in seven to the X minus six equals zero and seven to the X plus eight equals zero. Now, we did software X add six both sides to get seven to the X equals six, seven to the X equals negative P on the other side. Now, we need natural log on both sides. So we'll take the natural log of both sides. In this case, Ellen raised the seven X equals Ellen six and Ellen raised the seven X equals felon negative heats. We can write L in seven races of the X S XL N seven on the right side. Same thing XL N seven will be equals to L N negative eight. Now we notice here we have an Ellen of negative eights natural log always has a positive X value and stomach. L and X always has to be greater than zero or X. That means we will disregard our answer on the right with the L in negative eight, we can then solve our XL N seven equals L N six by dividing by L N seven on both sides. We then get X equals L N six divided by L N seven. If you don't want to simplify any further start, final answer corresponds to answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 5^2x + 3(5^x) = 28

Key Concepts

Exponential Equations

Substitution Method

Rational and Irrational Numbers

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