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.

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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

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