Mathematics, 27.06.2019 05:20 photagraphykid

2^x=3^x+1 what are the exact approximate solutions

Answers: 3

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Answer from: Yvette538

Step-by-step explanation:

The goal of course is to solve for x. Right now there are 2 of them, one on each side of the equals sign, and they are both in exponential positions. We have to get them out of that position. The way we do that is by taking the natural log of both sides. The power rule then says we can move the exponents down in front.

$ln(2^x)=ln(3^{x+1})$ becomes, after following the power rule:

x ln(2) = (x + 1) ln(3). We will distribute on the right side to get

x ln(2) = x ln(3) + 1 ln(3). The goal is to solve for x, so we will get both of them on the same side:

x ln(2) - x ln(3) = ln(3). We can now factor out the common x on the left to get:

x(ln2 - ln3) = ln3. The rule that "undoes" that division is the quotient rule backwards. Before that was a subtraction problem it was a division, so we put it back that way and get:

$x(\frac{ln(2)}{ln(3)})=ln(3)$ . We can factor out the ln from the left to simplify a bit:

$x[ln(\frac{2}{3})]=ln(3)$ . Divide both sides by ln(2/3) to get the x all alone:

$x=\frac{ln(3)}{ln(\frac{2}{3}) }$

On your calculator, you will find that this is approximately -2.709

Answer from: Quest

answer: 1722

step-by-step explanation:

given: the mass of saturn= $5.685\times10^{26}\ kgs$

the mass of mercury= $3.302\times10^{23}\ kgs$

the number of times the mass of saturn is greater than the mass of mercury

$=\frac{\text{mass of saturn}}{\text{mass of mercury}}\\=\frac{5.685\times10^{26}}{3.302\times10^{23}}\\\\=1.72168\times10^{26-23}{by using law of exponent}]\\=1.72168\times10^3=1721.68\approx1722$

hence, the mass of saturn is 1722 times greater than the mass of mercury.

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.