solve the following equation?

Hi,

log 3^x - log 3^4 = 2

log (3^x / 3^4) = 2

(3^x / 3^4) = 10²

3^x / 81 = 100

3^x = 81 * 100 = 8100

x ln 3 = ln 8100

x = ln 8100 / ln 3

x = 8.1918

Hope this helps!
J

log(3^x) - log(3^4) = 2
(x)log(3) = 2 + log(3^4)
(x)log(3) = 2 + 4log(3)
x = [2 + 4log(3)]/[log(3)]
x = 2/[log(3)] + [4log(3)]/[log(3)]
x = 2/[log(3)] + 4

Log 3^x - Log 3^4 = 2
x Log 3 - 4 Log 3 = 2
(Log 3)(x - 4) = 2
x - 4 = 2 / Log 3
x = (2 / Log 3 ) + 4
x = 8.19

log [ 3^x / 3^4 ] = 2

3^x / 3^4 = 100--------------------( using base 10 logs )

3^x = 8100

x log 3 = log 8100

x = log 8100 / log 3

x = 8.192

log3^x-log3^4=2
x log(3) - 4 log(3) = 2
x log(3) = 2+4 log(3)
x = (2 + 4 log(3)) / log(3)

Substitute log(3)=0.47712125 and simplify:

x= 8.1918

OK

log3^x-log3^4=2

Log(a)-Log(b) is the same as Log(a/b)

so Log(3^x/3^4)=2

so Log(3^(x-4))=2

(x-4)(Log(3))=2

x-4=2/(Log(3)
x= 2/(log3)+4

x= 8.192 approx assuming logs to base 10

log (3^x / 3^4) = log 9
x-4 = 2
x = 6