SOLUTION: 3 to the (A) power = 800, what is (A)

Algebra ->  Exponents -> SOLUTION: 3 to the (A) power = 800, what is (A)      Log On


   

Question 156427: 3 to the (A) power = 800, what is (A)
Found 3 solutions by Earlsdon, gonzo, Ms.Smith:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for A:
3%5EA+=+800 Take the logarithm of both sides.
log%28%283%29%29%5EA+=+log%28%28800%29%29 Apply the power rule for logs to the left side: log%28%28a%29%29%5En+=+n%2Alog%28%28a%29%29
A%2Alog%28%283%29%29+=+log%28%28800%29%29 Divide both sides by log%28%283%29%29
A+=+%28log%28%28800%29%29%29%2Flog%28%283%29%29 Evaluate using your calculator.
A+=+6.0846

Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
3 to the a power = 800 if and only if log 800 to the base 3 = a.
trick is to use the conversion formula so the calculator can be used to solve the problem.
the trick?
log of x to the base b = log of x to any other base / log of base b to that other base.
so .................
log of 800 to the base 3 = log of 800 to the base 10 / log of 3 to the base 10.
now the calculator can be used.
take log of 800 and divide it by log 3.
get 2.903... / .477 ...
becomes 6.08459...
so log of 800 to the base 3 = 6.08459 .......
if and only if 3 to the 6.08459... power = 800.
put in calculator 3 to the 6.08459 power and get 800.
conversion works with any other base.
can use ln for example (natural log to the base e).
log 800 to the base 3 = ln 800 / ln 3.
solve in calculator and get 6.08459 .....
same answer as when used base 10.
so formula for conversion again is ....................
log of x to the base b = log of x to the base a / log of b to the base a
where
b is the original base.
a is any other base.











Answer by Ms.Smith(3) About Me  (Show Source):
You can put this solution on YOUR website!
IN ORDER TO FIND OUT WHAT A IS YOU HAVE TO DIVIDE 800 BY 3.
SO 800 DIVIDED BY 3 IS 266.6 SO A=266.6