How do you find the solution of the exponential equation 10^(1 - x) = 6^x ?

We can use logarithms to solve exponential
equations.

We'll take the common logarthim both
sides:

lg 10^(1 - x) = lg 6^x

We'll
apply the power rule for logarithms:

(1-x) lg 10 = x lg
6

We'll recall that lg 10 = 1

We'll
re-write the equation:

1 - x = x lg
6

We'll add x  both sides:

x + xlg6 =
1

We'll factorize by x:

x(1 + lg 6) =
1

We'll divide by 1 + lg 6 = lg 10 + lg 6 = lg
60:

x = 1/lg 60

Rounded to four decimal
places:

x =
0.5624