7x - 2 = 5x
Take logarithms of both sides:
log(7x - 2) = log(5x)
Use a rule of lagarithms that allows an exponent to come
out in front as a multiplier
(x - 2)log(7) = x·log(5)
To make the algebra less bulky and cumbersome,
let A = log(7) and B = log(5), then we have
(x - 2)A = x·B
A(x - 2) = Bx
Ax - 2A = Bx
Get both x terms on the left side
and the non-x term on the right side:
Ax - Bx = 2A
Factor out x
x(A - B) = 2A
Divide both sides by (A - B)
= =
x =
Substitute log(7) for A and log(5) for B
x =
x = 11.56654212 round to 11.5665
Edwin
