Algebra 2

7^(3*x-1)=5^(x-1)   take the log of both sides

log [7]^(3*x-1) = log [ 5]^(x-1)    and we can write this as

(3x - 1)log7  = (x-1)log 5   expand

3x log7  - log 7  = xlog 5 - log 5      rearrange

3x log 7 - x log 5  = log7 - log 5     factor out x on the left side

x [ 3 log 7 - log 5] = log 7 - log 5     divide both sides by [ 3 log 7 - log 5]

x = [ log7  - log 5] / [ 3log 7 - log 5]    = about .0796

Similarly:

7^(3x-1) =5^(x-1)

LOG both sides

(3x-1)Log7 = (x-1)Log5  Simplify

(3x-1)/(x-1) = log5/log7=.82708

3x-1 = .82708x - .82708

2.1729x=.1729

x=.07957