Question

Solve each equation or inequality.
CLICK

Answer 1

\[5^{X}=4^{x+3}\]

Answer 2

Do you remember the property of logarithms that \(\log a^x = x \log a\)? That should give you a clue as to how to proceed...

Answer 3

log both sides.

Answer 4

in depth explanation please ?

Answer 5

@whpalmer4 gave you a pretty good explanation. Lol

Answer 6

\[\log 5^x = \log 4^{x+3}\]\[x \log 5 = (x+3) \log 4\]
Solve for \(x\)

Answer 7

i dont know what to do from there honestly.

Answer 8

What do YOU think your next step should be?
You won't understand unless you try it and make mistakes first.

Answer 9

divide both sides by x and you're left with log 5= 3 log 4 ?

Answer 10

I like your thinking, but not quite. Since you are solving for "x". It must be in the form:

x = ____

hence, you can't cancel out x.
First step is to distribute the log(4) across the parenthesis.

Answer 11

put all your constants on one side, and put the x's on the other side.

Answer 12

x^2= 3log 4 x 3 log 5 ?

Answer 13

No. I don't know where you got the x squared, but you should get this:
\[xlog(5) = xlog(4)+3\log(4)\]
Now, notice that you have TWO log's with x's. Which means that you can subtract it!
\[xlog(5)-xlog(4) = 3\log(4)\]
now, what do you think is the next step?
[HINT: you have to factor OUT something...]

Answer 14

factor out the x ?

Answer 15

Correct. Now you'll have: \[x[\log(5)-\log(4)]=3\log(4)\]
now, if you want to solve for "x". What do you think you should do now to get x by itself?

Answer 16

divide ?

Answer 17

Great.

Answer 18

....

Answer 19

What did you divide by? If you divided correctly, you should see that you have now arrived at your answer.

Answer 20

divide both sides by 4 ?

Answer 21

No. Why would you divide by 4? You would divide everything EXCEPT x. yOU ARE Trying to solve for x.

Answer 22

\[x = \frac{ 3\log(4) }{ \log(5)-\log(4) }\]

Answer 23

okay, thats my final answer ? i wouldnt simplify anything ?

Answer 24

yes...

Answer 25

thank you !