Question

Solve 5^x + 5 = 9^x
Help please..? @Zarkon

Answer 1

you have to solve it numerically

Answer 2

Here is the first step... \[x+5 \log5=x \log 9\] Then you use the calculator to find the logs of 9 and 5. That's where I get stuck.

Answer 3

you will have to solve that numerically too,

Answer 4

Ok, how would I do that?

Answer 5

use a calculator or computer program that has a solve function

Answer 6

\[x(\log(9)-1)= 5\log5\]

Answer 7

so re-arrange for x and solve with calculator

Answer 8

oops...or do that...for some reason when I wrote is down to do I put 5log(x) ;)

Answer 9

So you find what the log of 9 and 5 is then you distribute that to the coefficients?

Answer 10

Hold on - I think golf4lifes's formula may be wrong...

Answer 11

@Golf4Life, the way you attempted to isolate x is not correct.

Answer 12

I agree - hold on there....

Answer 13

ok, so log5= 0.6989700x+ 5.6989700=log9=0.9542425x ..How do you simplify from here on?

Answer 14

if you take logs of both sides you have

log(5^x+5) i.e. log(a+b)

Now, this is NOT equal to loga + logb, and is not generally able to be simplified (afaik)

So - can I ask you to check the question:

Is it
\[5^{(x+5)}\]

or
\[5^{x}+5\]

Answer 15

Yes it is the first one, 5^(x+5) @MrNood

Answer 16

Ok - that makes quite a difference

\[5^{x+5}=9^{x}\]
\[(x+5)\log(5)=xlog(9)\]

\[xlog(5)+5\log(5)=xlog(9)\]
\[x(\log(5)-\log(9))=-5\log(5)\]

Answer 17

is it -3.63?

Answer 18

If that's what it is then:

\[5^{x + 5} = 9^x\]
\[5^x5^5 = 9^x\]
\[\frac{5^x}{9^x}\dot\ 5^5 = 1\]
\[\frac{5^x}{9^x} = \frac{1}{5^5}\]

\[\left(\frac{5}{9}\right)^x = \frac{1}{5^5}\]
\[\log{\left(\frac{5}{9}\right)^x} = \log\left({\frac{1}{5^5}}\right)\]
\[x\log{\left(\frac{5}{9}\right)} = \log\left({\frac{1}{5^5}}\right)\]
\[x = \frac{\log(1/5^5)}{\log(5/9)}\]
\[x = \frac{\log(1) - 5\log(5)}{\log{5} - \log{9}}\]
\[x = -\frac{5\log(5)}{\log{5} - \log{9}}\]

Answer 19

log9>log5 so LHS is -ve
RHS is -ve
so answer must be +ve

Answer 20

be sure to notice the minus sign on Hero's equation - otherwise it is the same as my approach

Answer 21

?

Answer 22

x ≈ -3.63
x ≈ -0.28
x ≈ 0.07
x ≈ 13.69
These are the choices. When I put Hero's equation into the calculator I get -4.05

Answer 23

@Hero

Answer 24

When I put my answer into my calculator, I get one of the answer choices.

Answer 25

@Golf4Life, I expressed x in three different ways. You should test them all out in your calculator.

Answer 26

Each result should be the same.

Answer 27

I put each of your problems in, maybe I am entering them wrong.\[x = \frac{\log(1) - 5\log(5)}{\log{5} - \log{9}}\] So for this one the top would be \[x=-3.49485\-0.25527\] Is that right? That should equal=-3.75 Which is choice (a)?

Answer 28

Yep, you're confused about something.

Answer 29

What kind of calculator do you have?

Answer 30

I was using my iPhone. Should I use my Texas instrument one instead?

Answer 31

Uh...ya. Your iPhone is not a replacement for your TI

Answer 32

As a matter of fact, I use a TI Nspire. I recommend you get one as well.

Answer 33

I have the TI-30XA. So how I put the equation in was it correct?

Answer 34

If you didn't get the correct answer, then no, it isn't correct.

Answer 35

Which is the correct one then?

Answer 36

On both calculators I am getting the same thing:/

Answer 37

@Hero?

Answer 38

Probably because you're entering the same incorrect information into both calculators. I remember when I was your age. I used to do the same thing. It's a phase. You'll grow out of it (hopefully).

Answer 39

Hang on a minute...let me help you out a bit.

Answer 40

http://www.wolframalpha.com/input/?i=-%285+log%285%29%29%2F%28log%285%29+-+log%289%29%29

Answer 41

This is how you enter it into your calculator:
-(5 log(5))/(log(5) - log(9))

Answer 42

It has to be entered exactly like that or you won't get the right answer.

Answer 43

Here's the other form I presented x:

http://www.wolframalpha.com/input/?i=+log%281%2F5%5E5%29%2F%28log%285%2F9%29

And I entered:
log(1/5^5)/(log(5/9)

I got the same result again

Answer 44

You are right! I put it in the way you said and I got 13.69. Thanks @Hero! How did you get so good at this stuff? :)

Answer 45

The more familiar you become with something, the more comfortable you are with it.

Answer 46

Haha ok thanks again!