Logarithmic functions help?

Take the log of both sides which allows you to bring down the exponent so that you get (x+2)log5=(x-1)log7

Then just do log7/log5=(x+2)/(x-1). Simplify and multiply one x term back over to get 1.21x-1.21=x+2. Rearrange some terms to get .21x=3.21. x=15.28

——————————————————————————————————————

         5^(x+2) = 7^(x-1)

   log(5^(x+2)) = log(7^(x-1))

    (x+2) log(5) = (x-1) log(7)

x log5 + 2 log5 = x log7 - log7

x log5 - x log7 = -2 log5 - log7

(log5 - log7)x = -(2 log5 + log7)

                          -(2 log5 + log7)

                  x = ————————

                            (log5 - log7)

                          2 log5 + log7

                  x = ———————

                            log7 - log5

Have a good one!

——————————————————————————————————————

Take logs of both sides and you have (x + 2)*log5 = (x - 1)*log7 so from a calculator you will get 0.69897(x + 2) = 0.845098(x - 1) and that gives us 0.69897x + 1.39794 = 0.845098x - 0.845098 and that becomes 1.39794 + 0.845098 = 0.845098x - .0.69890. or 0.146128x = 2,243039 so x = 15.349816... - round that off as you see fit.

5^(x + 2) = 7^(x - 1)

Take logs of both sides (any base)

(x + 2)log(5) = (x - 1)log(7)

Distribute

x log(5) + 2log(5) = x log(7) - log(7)

x(log(7) - log(5)) = 2 log(5) + log(7)

x log(7/5) = log(25) + log(7) = log(175)

x = log(175)/log(7/5) ≈ 15.35