can you help me solve for n? please show work.?

Question

5400 = 2000 (1+.18)^n

Answer 1

I thought that you'd only use ln as the inverse of e (like if you had e^n (which would represent continuity)), but I'm not sure.
This is what I got using logs:

First I divided both sides by 2000 and simplified:
5400/2000 = (1 + 0.18)^n
2.7 = 1.18^n

Then I found the log1.18 of both sides, knowing that the log1.18 of 1.18 would cancel out and bring down the n:
log1.18 of 2.7 = log1.18 of 1.18^n
log1.18 of 2.7 = n
Since Logs have to have a base of 10 to use on your calculator you can change log1.18 of 2.7 to the following:
Log of # over Log of the Base

So that gives you:
Log2.7/Log1.18

You can plug that into your calculator and you get:
aprox. 6.00099775, which rounds off to 6!
^_^

Answer 2

You have to be able to use logs. First, divide by 2000

5400/2000=(1+.18)^n

then, combine 1+.18 into 1.18 to get
5400/2000=(1.18)^n
Then, take the log base 1.18 of both sides to get
log1.18(5400/2000)=nlog1.18(1.18), which means your answer is just log1.18(5400/2000), which equals in decimal 6.00099775. Hope this helps!

Answer 3

5400 = 2000 (1 + 0.18)^n

Divide both sides by 2000,

5400/2000 = (1.18)^n

2.7 = (1.18)^n

To solve for n, you have to convert this to logarithmic form.

log[base 1.18](2.7) = n

But, to make this calculator friendly, we have to use the change of base formula. Choosing base e,

ln(2.7) / ln(1.18) = n

Punching this into your calculator will get you an approximation.

Answer 4

5400/2000 = (1 + .18)^n

2.7 = 1.18^n

log-1.18(2.7) = n

We convert this to a base-10 log

log-10 (2.7) / log-10 (1.18) = n

.43 / 0.07 = 6

Answer 5

5400 = 2000 (1+.18)^n
Take ln of both sides:
ln(5400) = ln[2000 (1+.18)^n]
Multiplication rule for ln:
ln(5400) = ln(2000) + ln[(1+.18)^n]
Exponent rule for ln:
ln(5400) = ln(2000) + n ln(1+.18)
Subtract ln(2000) from both sides:
ln(5400) - ln(2000) = n ln(1+.18)
Divide ln(1.18) from both sides:
[ln(5400) - ln(2000)] / ln(1.18) = n
Evaluate:
(8.594 - 7.609) / 0.166 = n
n = 5.93

Answer 6

5400=2000(1+.18)^n
5400/2000=(1.18)^n
2.7=(1.18)^n
Taking logarithm,
log 2.7=[log (1.18)^n]
log 2.7=n(log 1.18)
0.4314=n(0.0719)
n=0.4314/0.0719
n=6.
I think the value is somewhere near 6, since log values are not exact.

Answer 7

5400=2000(1+1.18)^n
5400=2000(1.18)^n
5400/2000 = (1.18)^n
2.7 = (1.18)^n
ln (2.7) = n ln(1.18)
n= ln (2.7) / ln(1.18)
or n= about 6