Question

2^x+3=5^x
If someone could take me step by step in this problem????

Answer 1

okay, so in this problem, you have to be familiar with the log function (which i assume you are)

Answer 2

A little, thats what we are learning now

Answer 3

I know that I have to natural (ln) each side..

Answer 4

I came up with an answer of 2.269 I just know its wrong...

Answer 5

if someone is good with vectors here, so plz give some thought to my question as well.

Answer 6

sorry, logs are so far back in my math knowledge. im trying to remember the rules

Answer 7

\[2^x+3=5^x\] or \[2^{x+3}=5^x\]

Answer 8

Here is my work... maybe someone can check it to see where I went wrong.

2^(x+3)=5^x

Then I divided each side by x ln 2 and it left me with:

x+3/x=ln5/ln2

Answer 9

The second one...

Answer 10

ohhh i remember how to do it. i thought it was 2^x + 3 instead of 2^(x+3)

Answer 11

I dont know how to write equations on here.... so sorry

Answer 12

its cool. alright, so log both sides to start. that will get you ln(2^(x+3)) = ln(5^x)

Answer 13

then with the logarithm rules, you can bring the exponent of both sides in front. this gives you: (x+3)ln(2) = xln(5)

Answer 14

then you switch things around to get (x+3)/x = ln(5)/ln(2)

Answer 15

Ok, I got that. So far, so good

Answer 16

then you can split the fraction on the left up to make two different ones. It becomes (x/x) + (3/x)

Answer 17

or, in other words, (3/x) + 1

Answer 18

OK... right here is where my teacher told us to croos multiply?

Answer 19

cross sorry. So it gave me x+3/x=2.322/1

Answer 20

does your teacher want you to get an exact answer? or are decimals okay

Answer 21

Decimals to the thousandth

Answer 22

okay, well i would highly recommend solving for x in exact form first, and then getting the decimal. it's much more pure math. if you have (x/3) + 1 = ln(5)/ln(2) it's very easy to get it to exact form

Answer 23

sorry, (3/x)

Answer 24

just move the 1 over to the right side

Answer 25

What one? where are you getting the one from?

Answer 26

then it will be 3/((ln(5)/ln(2))+1)

Answer 27

from the left side. where it says (3/x) + 1 = ln(5)/ln(2)

Answer 28

it becomes 3/x = ln(5)/ln(2) -1

Answer 29

which becomes 3/((ln(5)/ln(2))-1)

Answer 30

^^ that is equal to x

Answer 31

is the answer 1.689?

Answer 32

i believe its 2.269. make sure you plug it in correctly on your calculator.

Answer 33

Thats what I had for my answer to begin with?

Answer 34

So I am right?

Answer 35

haha, yes

Answer 36

Thanks for your help.

Answer 37

no problem