Find the solution of the equation 5^(11x-1)=7^x

Since the bases are not matching, we can use logarithms to
solve exponential equations.

We'll take logarthims both
sides:

log5  [5^(11x-1)] = log5
(7^x)

We'll apply the power rule for
logarithms:

(11x-1) log5 5 = x log5
7

We'll recall that log5 5 =
1

We'll re-write the
equation:

11x-1 = x log5
7

We'll subtract x log5 7  both
sides:

11x - x log5 7 =
1

We'll factorize by x:

x(11 -
log5 7) = 1

We'll re-write log5 7 =
lg7/lg5

x(11 - lg7/lg5) =
1

We'll divide by 11 - lg7/lg5 =
9.7909

x = 1/9.7909

Rounded to
four decimal places:

x =
0.1021