Question

625^x=3125

Answer 1

\[x=\frac{\ln(3125)}{\ln(625)}\]

Answer 2

you solve
\[b^x=A\] for x in one step via
\[x=\frac{\ln(A)}{\ln(b)}\]

Answer 3

if 3125 is an integer power of x then you can guess perhaps

Answer 4

i mean if 3125 is an integer power of 625

Answer 5

but it is not

Answer 6

ok so now what?

Answer 7

625 = 5^4, 3125 = 5^5. Take log(5) of both sides to get
x log(5)(5^4) = log(5)(5^4)
4x = 4
x = 1.

Answer 8

oops
x log(5)(5^4) = log(5)(5^5)
4x = 5
x = 5/4

Answer 9

too much work. whip out mr calculator and type in
\[\frac{\ln(3125)}{\ln(625)}\] you will get
\[\frac{5}{4}\]

Answer 10

although of course abtrhearn is right. but if you recognize that
\[625=5^4\] and
\[3125=5^5\] you do not need logs. just write
\[5^{4x}=5^5\] so
\[4x=5\] and
\[x=\frac{5}{4}\]