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

- anonymous

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

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- jamiebookeater

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- anonymous

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

- anonymous

A little, thats what we are learning now

- anonymous

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

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## More answers

- anonymous

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

- anonymous

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

- anonymous

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

- nikvist

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

- 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

The second one...

- anonymous

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

- anonymous

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

- anonymous

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

- 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

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

- anonymous

Ok, I got that. So far, so good

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

Decimals to the thousandth

- 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

sorry, (3/x)

- anonymous

just move the 1 over to the right side

- anonymous

What one? where are you getting the one from?

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

^^ that is equal to x

- anonymous

is the answer 1.689?

- anonymous

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

- anonymous

Thats what I had for my answer to begin with?

- anonymous

So I am right?

- anonymous

haha, yes

- anonymous

Thanks for your help.

- anonymous

no problem

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