anonymous
  • anonymous
2^x+3=5^x If someone could take me step by step in this problem????
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
okay, so in this problem, you have to be familiar with the log function (which i assume you are)
anonymous
  • anonymous
A little, thats what we are learning now
anonymous
  • anonymous
I know that I have to natural (ln) each side..

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anonymous
  • anonymous
I came up with an answer of 2.269 I just know its wrong...
anonymous
  • anonymous
if someone is good with vectors here, so plz give some thought to my question as well.
anonymous
  • anonymous
sorry, logs are so far back in my math knowledge. im trying to remember the rules
nikvist
  • nikvist
\[2^x+3=5^x\] or \[2^{x+3}=5^x\]
anonymous
  • anonymous
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
anonymous
  • anonymous
The second one...
anonymous
  • anonymous
ohhh i remember how to do it. i thought it was 2^x + 3 instead of 2^(x+3)
anonymous
  • anonymous
I dont know how to write equations on here.... so sorry
anonymous
  • anonymous
its cool. alright, so log both sides to start. that will get you ln(2^(x+3)) = ln(5^x)
anonymous
  • anonymous
then with the logarithm rules, you can bring the exponent of both sides in front. this gives you: (x+3)ln(2) = xln(5)
anonymous
  • anonymous
then you switch things around to get (x+3)/x = ln(5)/ln(2)
anonymous
  • anonymous
Ok, I got that. So far, so good
anonymous
  • anonymous
then you can split the fraction on the left up to make two different ones. It becomes (x/x) + (3/x)
anonymous
  • anonymous
or, in other words, (3/x) + 1
anonymous
  • anonymous
OK... right here is where my teacher told us to croos multiply?
anonymous
  • anonymous
cross sorry. So it gave me x+3/x=2.322/1
anonymous
  • anonymous
does your teacher want you to get an exact answer? or are decimals okay
anonymous
  • anonymous
Decimals to the thousandth
anonymous
  • anonymous
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
anonymous
  • anonymous
sorry, (3/x)
anonymous
  • anonymous
just move the 1 over to the right side
anonymous
  • anonymous
What one? where are you getting the one from?
anonymous
  • anonymous
then it will be 3/((ln(5)/ln(2))+1)
anonymous
  • anonymous
from the left side. where it says (3/x) + 1 = ln(5)/ln(2)
anonymous
  • anonymous
it becomes 3/x = ln(5)/ln(2) -1
anonymous
  • anonymous
which becomes 3/((ln(5)/ln(2))-1)
anonymous
  • anonymous
^^ that is equal to x
anonymous
  • anonymous
is the answer 1.689?
anonymous
  • anonymous
i believe its 2.269. make sure you plug it in correctly on your calculator.
anonymous
  • anonymous
Thats what I had for my answer to begin with?
anonymous
  • anonymous
So I am right?
anonymous
  • anonymous
haha, yes
anonymous
  • anonymous
Thanks for your help.
anonymous
  • anonymous
no problem

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