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Solve the following equations for % You do not need to calculate the answers just show whatyou would plug into the calculator: 2 = logx - 3 4(9*)c.) 2*-8 =}4) In(e/...

Question

Solve the following equations for % You do not need to calculate the answers just show whatyou would plug into the calculator: 2 = logx - 3 4(9*)c.) 2*-8 =}4) In(e/x)? = 14

Solve the following equations for % You do not need to calculate the answers just show whatyou would plug into the calculator: 2 = logx - 3 4(9*) c.) 2*-8 =} 4) In(e/x)? = 14



Answers

Solve each logarithmic equation. Be sure to reject any value of $x$ that is not in the domain of the original logarithmic expressions. Give the exact answer. Then, where necessary, use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution.
$$\log (x+3)+\log (x-2)=\log 14$$

Okay, so we'll stop by using our product. Girls. So we have experts three times X monies to that's X squared plus X minus six. And now by our uniqueness property, we know that our insides are equal to each other, but it's attract 14 on both sides. So we have six plus 14. That's equal to 20. So we get minus 20 is equal to girl. And now we conduct Buddhist into X plus five times X minus four. Okay, so we get that X is equal to negative five. But if you like this end, we get log of a negative value. Looks will exclude that, and we just get X is equal to four for our solution.

Just all this equation in The first thing I'm going to do is combine these logs into a single law, Guerry them using the product rule so we get the log of the product. X plus three times X minus two equals a lot of 14. And because we have log on both sides, we can use the 1 to 1 property to write the equation without logger them's so it would be X plus three times X minus two equals 14. Let's go ahead and multiply that out and we have X squared plus X minus six equals 14. So we have a quadratic equation to solve. Let's subtract 14 from both sides. X squared plus X minus 20 equals zero, and we can factor it into X plus five times X minus four. And when we set each factor equal to zero and solve each of these equations, we have X equals negative five and X equals positive for. But just keep in mind that log arrhythmic functions have a restricted domain, so X plus three has to be positive and X plus X minus two has to be positive. Therefore, X could not be negative. Five positive four works

Okay, So notice that we have logged weighs three on both sides and very nicknames. Property. That must mean that experts for is you could to seven subtracting four on both sides. We get that exit to three.

Okay. We have law based three of X Plus four equals law based three of seven. And since we have logged based three on both sides, we can use the Oneto one property to write the equation. Without logarithms, it would be X plus four equal seven subtract four from both sides and we get X equals three.


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