Suppose 5^{3x+2} = 675. Find 5^x

Take LOG of both sides to get:

(3x+2) LOG 5 = LOG 675    solve for x

3x+2 = log 675/log5

x=.682606194

5^.682606194 =~3

Thanks, EP....here's a slighly different approach...

5^(3x + 2)  = 675     and we can write

5^2 * 5^(3x)  = 675      simplify

25 * 5^(3x)  = 675      divide both sides  by 25

5^(3x)  = 27     and we can write

(5^x)^3  = 27     take the cube root of both sides

5^x  = 3