- #1

- 11

- 0

## Homework Statement

2^x+3^x=13, x=2. How do i prove it?

## The Attempt at a Solution

i did this

x log 2 + x log 3 = log 13

x(log 2 + log 3)=log 13

x(0.301+0.477)= 1.11

0.778x=1.11

x=1.43

- Thread starter Champdx
- Start date

- #1

- 11

- 0

2^x+3^x=13, x=2. How do i prove it?

i did this

x log 2 + x log 3 = log 13

x(log 2 + log 3)=log 13

x(0.301+0.477)= 1.11

0.778x=1.11

x=1.43

- #2

HallsofIvy

Science Advisor

Homework Helper

- 41,833

- 956

[itex]2^x+ 3^x= 2^2+ 3^2= 4+ 9= 13[/itex].

You are not asked so solve the equation!

- #3

tiny-tim

Science Advisor

Homework Helper

- 25,832

- 251

(try using the X

Nooo …x log 2 + x log 3 = log 13

that's log (x

- #4

- 11

- 0

Actually i know that the answer x=2 but how am i suppose to prove it?

- #5

tiny-tim

Science Advisor

Homework Helper

- 25,832

- 251

If the question says "show that 2

- #6

Mark44

Mentor

- 33,722

- 5,418

You can't get the equation above from the one you started with. log(A + B) [itex]\neq[/itex] logA + logB. What you did was to take the log of both sides to get## Homework Statement

2^x+3^x=13, x=2. How do i prove it?

## The Attempt at a Solution

i did this

x log 2 + x log 3 = log 13

log(2^x + 3^x) = log 13. That's a legitimate step, but it doesn't lead you anywhere.

The problem is that log(2^x + 3^x) [itex]\neq[/itex] log 2^x + log 3^x.

x(log 2 + log 3)=log 13

x(0.301+0.477)= 1.11

0.778x=1.11

x=1.43

- #7

- 11

- 0

Is there any way to solve this question by calculation?

Thanks.

Thanks.

- #8

tiny-tim

Science Advisor

Homework Helper

- 25,832

- 251

Nope.

- #9

- 186

- 0

Champ, read this quote again. There are only two options:^{x}+ 3^{x}= 13", then there's no exact way of doing it, you'll have to use an approximation method (or guess).

If the question says "show that 2^{x}+ 3^{x}= 13 has a solution x = 2", or "prove that 2^{x}+ 3^{x}= 13 has a solution x = 2", then all you need to do is to show that 2^{2}+ 3^{2}= 13.

1) "Solve..." or

2) "Show that"/"Prove..."

There's a phrase that comes up frequently in math (that honestly kinda p*sses me off!)...

This means "I can SEE the answer, but I can't/won't show HOW you could get the same answer without guessing". There might be a better description out there for this phrase, which I think applies to our situation.

We can see that x = 2 is a solution. We can see that it is a UNIQUE solution because increasing/decreasing x will increase/decrease BOTH terms on the left hand side of the equation...

- Last Post

- Replies
- 2

- Views
- 345

- Last Post

- Replies
- 10

- Views
- 1K

- Last Post

- Replies
- 28

- Views
- 9K

- Replies
- 1

- Views
- 4K

- Last Post

- Replies
- 0

- Views
- 671

- Last Post

- Replies
- 11

- Views
- 2K

- Last Post

- Replies
- 1

- Views
- 1K

- Last Post

- Replies
- 0

- Views
- 1K

- Last Post

- Replies
- 2

- Views
- 1K

- Last Post

- Replies
- 6

- Views
- 1K