3^x+4=7^x-1

Question

3^x+4=7^x-1

anonymous · Answer

my guess is this is 
$$\large 3^{x+4}=7^{x-1}$$am i right?

anonymous · Answer

It's an exponent

anonymous · Answer

is it the question i wrote?

anonymous · Answer

Yes

anonymous · Answer

then start with 
$$\large (x+4)\ln(3)=(x-1)\ln(7)$$ then do a raft of algebra to solve for $x$

anonymous · Answer

Do you mind helping me a little bit more? I have just started to do these and don't understand how they work. I've watched videos but still don't get it.

anonymous · Answer

no i don't mind
first step is to write what i wrote above $$\large (x+4)\ln(3)=(x-1)\ln(7)$$ now $\ln(3)$ and $\ln(7)$ are just numbers, so to solve for $x$ we have to multiply out first to get rid of the parentheses

anonymous · Answer

we get 
$$x\times \ln(3)+4\ln(3)=x\times \ln(7)-\ln(7)$$ when you remove the parentheses
okay so far

anonymous · Answer

Yes I understand.

anonymous · Answer

ok now as usual to solve for $x$ you need everything with an $x$ on one side of the equal sign, everything else on the other
it doesn't really matter which side you put it on, but i will subtract $x\times \ln(7)$ from both sides to get 
$$x\ln(3)-x\ln(7)+4\ln(3)=-\ln(7)$$

anonymous · Answer

then the part without an $x$ should go on the other side, subtracting $4\ln(3)$ from both sides gives 
$$x\ln(3)-x\ln(7)=-\ln(7)-4\ln(3)$$

anonymous · Answer

ok to that step? only two more

anonymous · Answer

Alright

anonymous · Answer

ok now we factor the $x$ out of the left so we can figure out what to divide by 
$$(\ln(3)-\ln(7))x=-\ln(7)-4\ln(3)$$

anonymous · Answer

then divide to get 
$$x=\frac{-\ln(7)-4\ln(3)}{\ln(3)-\ln(7)}$$

anonymous · Answer

there are lots of other ways to write this
so if you have a different answer in the book for example, don't get confused

anonymous · Answer

for example we could make it have less minus signs by writing 
$$x=\frac{\ln(7)+4\ln(3)}{\ln(7)-\ln(3)}$$

anonymous · Answer

Alrighty and I do online and well you don't get much information about the problems or a book but thank you for your help:)

anonymous · Answer

hope it was more or less clear
all the steps are there one at a time, so if you copy them you will have them to mimic for another such problem 

yw

anonymous · Answer

Okay thank you.