log56x7 log5x1 solved exponential formSolutionlog56x7 log5

log5(6x-7) + log5x=1 solved exponential form

log₅(6x-7) + log₅x=1

Using The log Property : logA + logB = log(A*B)

So, log₅( 6x -7)x =1

Now using the exponential property : log_ax = b ----> x = a^b

(6x -7)x = 5^1

6x^2 -7x -5 =0

Solving using quadratice root formula: x = ( 7 + /- sqrt( 49+120) )/12

= 7/12 + /- 13/12

x = 20/12 = 5/3 ; x = -4/12 = -1/3

Neglect x= -1/3 as -ve number is not in the domain of log function

Solution : x = 5/3