Exponents Inequalities

[deltoids]

I don't even know if that's what this type of problem is called but, here goes:

4^(x+3)=5^(x+2)

or

Would you use logs to solve for "x"? There isn't a specific problem like this is in my book, and I'm really confused.

Thanks in advance!

 

[stapel]

Would you use logs to solve for "x"?

Yes.

Take the log of your choice (but something your calculator can evaluate would probably be best). Take the powers out front. Distribute, and solve for x.

Eliz.

 

[deltoids]

Would you use logs to solve for "x"?

Yes.

Take the log of your choice (but something your calculator can evaluate would probably be best). Take the powers out front. Distribute, and solve for x.

Eliz.

Thank you so much for your reply!

So then, x+3log4=x+2log5

That's when things start stalling again, I don't know where to go from there..?

 

[Mrspi]

Thank you so much for your reply!

So then, x+3log4=x+2log5

That's when things start stalling again, I don't know where to go from there..?

Well, you are sort of on the right track....but I think some parentheses are needed here!

(x + 3) log 4 = (x + 2) log 5

Now, as Eliz suggested, you need to DISTRIBUTE:

x log 4 + 3 log 4 = x log 5 + 2 log 5

Get all of the terms containing x on one side of the equation, and the constants o the other side:

x log 4 - x log 5 = 2 log 5 - 3 log 4

Factor an x out of the two terms on the left side:

x(log 4 - log 5) = 2 log 5 - 3 log 4

Divide both sides of the equation by (log 4 - log 5):

x = (2 log 5 - 3 log 4) / (log 4 - log 5)

Now, it's calculator time......

I hope this helps you.

 

[deltoids]

Yes, it did, thank you so much! I had no idea about the distribution of logs there.