How do i solve this math problem?

[taco1435]

log base 3(x^2+11x) = log base 3(5)

how do i solve this?


EDIT: o and given the equation 3^x+2 = 5 ^2x identify three different ways to solve the problem. I dont actually have to solve it I just need to describe three different methods.

 

[Mo0o]

would'nt that imply x^2+11x =5?

 

[Sqube]

Yeah, it would.

 

[booger711]

quadratic formula x=(-11 +/- sqrt(11^2 +4*1*-5))/2

 

[taco1435]

thats what i thougt... about the first problem thanks
now can you help me with this?
given the equation 3^x+2 = 5 ^2x identify three different ways to solve the problem. I dont actually have to solve it I just need to describe three different methods.

 

[yankeesfan]

read wrong problem

 

[taco1435]

i know i can use log base 10 to bring down the exponents and then solve, but thats only 1 way... any help?

 

[dullard]

Originally posted by: taco1435
o and given the equation 3^x+2 = 5 ^2x identify three different ways to solve the problem. I dont actually have to solve it I just need to describe three different methods.

3^x + 2 - 5 ^2x = 0

1) Random guessing. Just keep guessing x-values until you get zero on the right-hand side.
2) Guided guessing, if you adjust x higher and the answer gets closer to zero, then adjust x even higher. If you adjust x higher and the answer gets farther from zero, then adjust x lower next time. And vise-versa.
3) Graph the thing on a computer/calculator. When it crosses the y-axis, you have your answer.

Note: These three solutions are commonly used for advanced math problems that you cannot solve any other way. Thus, by learning them you are far past your other students in your abilities to solve complex problems. They look the most simple, yet they are the most powerful. Don't let your teacher fool you into thinking you MUST do something more difficult.

 

[taco1435]

Originally posted by: dullard

Originally posted by: taco1435
o and given the equation 3^x+2 = 5 ^2x identify three different ways to solve the problem. I dont actually have to solve it I just need to describe three different methods.

3^x + 2 - 5^2 * x = 0

1) Random guessing. Just keep guessing x-values until you get zero on the right-hand side.
2) Guided guessing, if you adjust x higher and the answer gets closer to zero, then adjust x even higher. If you adjust x higher and the answer gets farther from zero, then adjust x lower next time. And vise-versa.
3) Graph the thing on a computer/calculator. When it crosses the y-axis, you have your answer.

Note: These three solutions are commonly used for advanced math problems that you cannot solve any other way. Thus, by learning them you are far past your other students in your abilities to solve complex problems. They look the most simple, yet they are the most powerful. Don't let your teacher fool you into thinking you MUST do something more difficult.

well, i that sounds good, but he never taught us anything like that. I think he's looking for different answers, but ill go with those unless someone else has any ideas?

 

[dullard]

Originally posted by: taco1435
well, i that sounds good, but he never taught us anything like that. I think he's looking for different answers, but ill go with those unless someone else has any ideas?

Help us out, which of the following did you intend to type:

A) 3^(x+2) = 5 ^(2*x)
B) (3^x)+2 = 5 ^(2*x)
C) 3^(x+2) = (5 ^2)*x
D) (3^x)+2 = (5 ^2)*x
E) Other.

I ask this because I bet what you typed is not what was being asked. The parenthesis really help when typing. However, we can solve any of those five problems if we just know what the problem is.

 

[taco1435]

O i meant to type option A.

 

[dopcombo]

Do your own homework.

But the answers u need for the 3 options is likely to be
a) quadratic equation involving b^2 - 4ac
b) complete the squares
c) factorisation

 

[Eeezee]

Originally posted by: dopcombo
But the answers u need for the 3 options is likely to be
a) quadratic equation involving b^2 - 4ac
b) complete the squares
c) factorisation

Quadratic formula doesn't really work here... the x is in the exponent

 

[dullard]

Originally posted by: taco1435
O i meant to type option A.

The standard method of solution would to be to take the log of either side. Choose any base you want as it doesn't matter. The rest is a piece of cake after you take the log of both sides.

Thats one more way for you. Heck, if your teacher is lenient, just use a few different bases and you'll get a few different methods all of which are basically the same.

 

[Kyteland]

One way to solve this is using the identities of exponents.

These are the identities you'll need, although there are more availible:
1) a^(b+c) simplifies to (a^b)*(a^c)
2) a^(b*c) simplifies to (a^b)^c
3) (a^b)/(a^c) = (a/c)^b

Your equation:
3^(x+2) = 5^(2x)
(3^x)*(3^2) = 5^(2x) // Using identity 1
9*3^x = 5^(2x) // Simple algebra
9*3^x = (5^2)^x // Using identity 2
9*3^x = 25^x // Simple algebra
9 = (25^x)/(3^x) // Simple algebra
9 = (25/3)^x // Using identity 3
x = log(base 25/3)(9) // Definition of log

A second way to solve this is to use the identities of logarithms. This is what dullard described.

These are the identities you'll need, although there are more availible:
1) log(base a)(a^b) = b
2) log(base a)(b^c) = c*log(base a)(b)

Your equation:
3^(x+2) = 5^(2x)
log(base 3)(3^(x+2)) = log(base 3)(5^(2x))
x+2 = log(base 3)(5^(2x)) // Using identity 1
x+2 = 2x*log(base 3)(5) // Using identity 2
x = 1/(log(base 3)(5)-1/2) // Simple algebra

Any time you want an exact answer to an equation like this you need to use identities to transform the complex equation in to simpler forms.

 

[taco1435]

wow thanks guys, Im gonna post my math more often here