If 3(x) + 243 = 2 (3(x)), what is the value of x?

[leovavassori]

Hello there,

my question relates to the ADVANCED Quant book - Pg 162 - Try it #6-2. It reads:

NOTE: (x) = number raised to "x" exponent.

If 3(x) + 243 = 2 (3(x)), what is the value of x? Solution:

If 3(x) + 243 = (3(x)) (3(x))

x = 5


How did the number 2 on the right side of the equation become (3(x))? I am guessing that its an estimated answer hence the 2 was brought up by 1 unit so that the equation could be manipulated?

Cheers,

Leo

[leovavassori]

Can anyone help please?

cheers,

Leo

[tim]

first, be careful bumping questions. every time you do that it puts the question at the absolute end of the queue for us to answer. bumping a question is the most effective way to cause a delay in getting your question answered..

as for the question, you are missing a plus sign. it should say:

If 3(x) + 243 = 2 (3(x))
3(x) + 243 = (3(x)) + (3(x))

notice that all we've done is take 2 times something and turn it into something plus something. this is always a valid step in algebra; in fact, that's what it means to multiply something by 2..

[leovavassori]

First thank you for answering. Second, what is a bumping question? I most certainly would like to know what its so that I can get questions answered quicker.

And with regards to your response:

"as for the question, you are missing a plus sign. it should say:

If 3(x) + 243 = 2 (3(x))
3(x) + 243 = (3(x)) + (3(x))

notice that all we've done is take 2 times something and turn it into something plus something. this is always a valid step in algebra; in fact, that's what it means to multiply something by 2.."


So what you did to the right side of the equation is the following:

i.e. 4 (3(x)) is the same as

(3(x)) + (3(x)) + (3(x)) + (3(x)) !?

Cheers,

Leo

[tim]

bumping a question is when you respond to your own post. then your post automatically becomes the newest one, which means it pushes it to the back of the line and you have to wait longer to get a response..

as for your question about the math, you are absolutely correct..

[metman82]

Even if I am still at the beginning with Book 1 and struggling with DS in number properties: I solved this as follows.

If 3^x + 243 = 2(3^x), what is the value of x?

Try to get the 3^x from the left side to the right side

243 = 2(3^x) - 1*3^x
rephrase it (place the 3^x outside the brackets (don't know the english word for this action))
243 = 3^x ( 2 - 1 )
You get
243 = 3^x
You know that 243 is a multiple of 3 ( 2+4+3 = 9).
3x3x3x3x3 = 3^5 = 243

I hope I understood this question correctly.
Maybe its not the best way to solve but I did it in 1 min.

[tim]

that works!